In fact...
The Apostles Are Repeatedly Portrayed as Having The Same level of Authority
Jesus said to them, "Truly I tell you, in the renewal of all things, when the Son of Man sits on His glorious throne, you who have followed Me will also sit on twelve thrones, judging the twelve tribes of Israel. (Matthew 19:28 BSB)
And in the church God has appointed first of all apostles, second prophets, third teachers, then workers of miracles, and those with gifts of healing, helping, administration, and various tongues. (1 Corinthians 12:28 BSB)
built on the foundation of the apostles and prophets, with Christ Jesus Himself as the cornerstone. (Ephesians 2:20 BSB)
The wall of the city had twelve foundations bearing the names of the twelve apostles of the Lamb. (Revelation 21:14 BSB)
In fact, Peter called himself "an apostle of Jesus Christ" in 1 Peter 1:1, and in chapter 5, writing to the "elders among you", he referred to himself as "as your fellow elder' (1 Peter 5:1).
The Equality of the Apostles in 1 Corinthians 1:12
Beginning in chapter 1 verse 10 Paul said the church was greatly divided in their opinion of their leaders. They were letting personal preferences and opinions actually cause quarrels amongst them. Paul mentions three prominent preachers stressing that none of them were worthy of special honor.
Individuals among you are saying, "I follow Paul", "I follow Apollos", "I follow Cephas", or "I follow Christ." (1 Corinthians 1:12 BSB)
Paul was painstakingly seeking to remind them that all the apostles were to be regarded as servants. As he asked "What then is Apollos? And what is Paul? They are servants through whom you believed, as the Lord has assigned to each his role. (1 Corinthians 3:5). Each of the apostles played a different but crucial role - one planted, one watered, but ultimately it was God who made it grow (3:6-9).
Christianity is not about following any human - be they Paul, Apollos, Peter or and certainly not the pope.
Besides which...
The Apostles Were Apparently Oblivious To Peter’s Supposed Superior Position
Then an argument started among the disciples as to which of them would be the greatest. (Luke 9:46 BSB) Also See Luke 22:24
I have become a fool, but you drove me to it. In fact, you should have commended me, since I am in no way inferior to those "super-apostles" (the most eminent apostles - NASB), even though I am nothing. (2 Corinthians 12:11 BSB)
Paul, an apostle - sent not from men nor by man, but by Jesus Christ and God the Father, who raised Him from the dead (Galatians 1:1 BSB)
But as for the highly esteemed - whatever they were makes no difference to me; God does not show favoritism — those leaders added nothing to me. On the contrary, they saw that I had been entrusted to preach the gospel to the uncircumcised, just as Peter had been to the circumcised.
or the One who was at work in Peter's apostleship to the circumcised was also at work in my apostleship to the Gentiles. And recognizing the grace that I had been given, James, Cephas, and John - those reputed to be pillars - gave me and Barnabas the right hand of fellowship, so that we should go to the Gentiles, and they to the circumcised. (Galatians 2:6-9 BSB)
Paul
Peter was very apparently a man of great courage, loyalty, and faith. Thus by virtue of his character he was eminently suitable to lead the charge of the earliest church. He was the spearhead - the driving force behind the original movement. And his preaching of the Gospel to both Jews and Gentiles were accompanied by quite a few miracles that provided corroborating evidence his words being God's truth.
However, once the Gospel was 'out there' in its embryonic form Peter had largely fulfilled a hugely important role but then pretty much went unmentioned until the Council of Jerusalem - a meeting of apostles and elders held around 48 - 50 CE to decide whether Gentile converts to Christianity had to follow the traditional Jewish laws of Moses (such as circumcision) to be saved.
It seems that Peter's very Biblical arguments convinced the gathering that it is through grace - not by obedience to the law - that both Jew and Gentile are saved (Acts 15:7-12) however, it was James who made the final decision (Acts 15:13-21).
It fell to others who took it to the next step and began establishing churches. Paul in particular took on a very prominent role establishing some 20 churches including those in Cyprus, Macedonia, Antioch, Philippi, Thessalonica, Corinth, the region of Galatia, Ephesus etc.
It took a man of extraordinary learning and ability to deal with the numerous and often complicated theological and other problems that arose in the various churches.
It took Paul.
Paul dealt with often the often unique challenges presented by the churches both in person and in writing - his letters to the churches making up a major portions of the New Testament canon.
Education
Paul was educated under Gamaliel (Acts 22:3) a Pharisee, a leader in the Jewish Sanhedrin, and one of the best known and most respected teachers in the late Second Temple period. He was also mentioned a couple of times in Scripture. Thus Paul had probably been educated beyond Torah expertise, to include a deep understanding of the Prophets and classical literature and philosophy. [07]
And the fact that he was a Roman citizen made everything he did and everywhere he went that much more possible
Citizenship
Additionally and very importantly, although from a Jewish family from the city of Tarsus, Pail was born a Roman citizen (Acts 16:37. 22:25-29) which gave him special legal protections, such as the right to a fair trial and the right to appeal his case directly to Caesar in Rome. (Roman law strictly forbade binding, whipping, or torturing a citizen without a formal trial and conviction).
He used this to his advantage in several cases.
For example, after expelling a demon from a fortune-telling girl, city officials illegally beat and imprisoned Paul and Silas. An earthquake freed them of their chains but, Paul and Silas refuse to leave quietly the next morning, politely insisting that their civil rights had been violated.
"After beating us in public without due process - men who are Romans - hey threw us into prison; and now they are releasing us secretly? No indeed! On the contrary, let them come in person and lead us out."
The officers reported these words to the chief magistrates. And they became fearful when they heard that they were Romans, and they came and pleaded with them, and when they had led them out, they repeatedly asked them to leave the city. (Acts 16:36-39 NASB)
The point being that Paul's citizenship was more than a just a passport. It
... gave Paul legal rights that protected him throughout his missionary journeys. On several occasions, Paul used these rights to defend himself and continue preaching the message of the Messiah.
Roman citizenship protected Paul from unfair treatment, but Paul used this privilege for a much greater purpose. Instead of seeking comfort or personal gain, he used his legal rights to continue sharing the good news throughout the Roman Empire. His citizenship opened doors to governors, kings, and even Caesar's court in Rome, allowing many more people to hear about Yeshua. What seemed like an ordinary legal privilege became one of the ways God helped spread the message of the Messiah. [08]
Without both his learning and the fact that he was a Roman citizen Paul would never have managed to accomplish all he did. Peter would have been severely handicapped.
BOTH men were an integral part of the spreading of the Gospel with very different roles to fill
Which brings us to the question of...
Who Founded The Church in Rome?
Although this is a question we may never be able to answer in this life, what we can be reasonably certain of is that neither Peter nor Paul did so.
Peter: Although the distinction was not absolute, the New Testament is very clear that Peter's primary mission was to the Jews while Paul was called to be the apostle to the Gentiles. As Paul wrote in his epistle to the Galatians
But on the contrary, seeing that I had been entrusted with the gospel to the uncircumcised, just as Peter had been to the circumcised (for He who was at work for Peter in his apostleship to the circumcised was at work for me also to the Gentiles), and recognizing the grace that had been given to me, James and Cephas and John, who were reputed to be pillars, gave to me and Barnabas the right hand of fellowship, so that we might go to the Gentiles, and they to the circumcised. (Galatians 2:7-9 NASB)
This brings up a relevant point. If the Pope is Peter's successor why isn't his mission also focused primarily on the Jews?
Paul: The earliest we even hear of a church in Rome comes from Paul's own letter to the Roman church that quite decidedly indicates that Paul had never even been to Rome at the time of writing. (This makes Romans a little different from most of Paul's other epistles which were written to churches he had himself established).
I do not want you to be unaware, brothers and sisters, that often I have planned to come to you (and have been prevented so far) so that I may obtain some fruit among you also just as among the rest of the Gentiles... So, for my part, I am eager to preach the gospel to you also who are in Rome. (Romans 1:13, 15 NASB)
What we do know is that when Paul wrote his letter to the Romans around 57 AD, he addressed an already existing community that he had never visited. Paul's letter also makes it clear that the church didn't have a single centralized leader but was made up of house churches - one said to be in Prisca and Aquila's home. (Romans 16:5)
The question that does arise however is if Paul had never visited Rome up to that point how is it that in verse 16 he sent personal greetings to a number of people by name. David Guzik puts forth a very likely possibility in his commentary on Romans
Even so, through mutual acquaintances or through his travels, Paul knew many of the Christians in Rome by name because he mentions them in Romans 16. Even if Paul only knew many of the Roman Christian by acquaintance, he knew two things about them and every true Christian. He knew they were beloved of God and that they were saints. [09]
Strikingly although Paul named around 28 people he sent greetings to he never mentioned Peter (in this verse or anywhere else in the letter).
If Peter were in Rome it is inconceivable that he would not have visited Paul at least one time. So why didn't Paul mention being paid a visit by the 'head of the Church'. It is even less believable that Luke who wrote of those times in fastidious detail never ever mentioned that Peter was in Rome - much less that he was heading up the church there.
Paul did however make two trips to Rome. The details of the first trip are lengthy but suffice to say Paul was arrested in Jerusalem after he was the focus of a riot in the temple. He was taken to Rome as a prisoner after appealing to Caesar and arrived in Rome around AD 59 - 60 after a dangerous sea voyage and shipwreck on Malta. Acts 28:30 tells us that Paul spent two years at Rome under house arrest in a rented home guarded by a Roman soldier.
... Paul stayed two full years in his own rented lodging and welcomed all who came to him, preaching the kingdom of God and teaching things about the Lord Jesus Christ with all openness, unhindered. (Acts 28:30-31 NASB)
How Did The Church In Rome Get Started?
The reality is that we do not know who started the church in Rome. It may well have been started simply by anonymous persons: since so many people traveled to and from Rome, it is not at all implausible that early converts to the faith (say, a decade or more before Paul wrote his letter to the Roman Christians in the 50s CE) returned to the capital and made other converts, and that the movement grew from there. [10]
Among the Jews visiting Jerusalem on the Day of Pentecost were visitors from Rome - both Jews and proselytes (Acts 2:10). Thus the most plausible scenario is that the Roman church was founded by people who heard Peter preach in Jerusalem and brought the faith back to Rome.
(Historically and traditionally proselyte is used most often to describe a non-Jew who converts to Judaism).
Rome became the center of church power because it was the capital of the empire not because Peter led it - for which there is absolutely no biblical nor historical support. The idea of a single supreme bishop emerged as the church became more organized in the 2nd century. The claim that Peter was the first pope was very likely used as justification for the Roman church's effort to assert authority over other Christian communities.
Conclusion
In summary there is no biblical justification or grounds to believe in apostolic succession.
There is absolutely no question that Peter was a man of great courage, loyalty, and faith - undoubtedly the reason he was given the keys to open the doors to both the Jews and the Gentiles.
He also pretty much led the charge in the earliest days after Jesus' resurrection
However, in the many many things written about Peter and what he accomplished not once is any mention made of Peter's supreme authority over the Church much less that he passed this authority down to his 'successors'. Nowhere does the text say or even imply the Roman Catholic understanding of Peter's successors.
Much to the contrary after spearheading the initial spread of the Gospel, Peter passed the baton onto Paul who not only who took it to the next step and established churches but shepherded those churches through their often unique challenges which Paul dealt with both in person and in writing.
These letters to the churches make up a large part of the New Testament canon.
Footnote I - Why Caesarea Philippi?
Caesarea Philippi is the source of one of the tributaries of the Jordan - the Banyas River. The Jordan River that played a central role in Scripture, begins its life-giving journey at the foot of Mt. Hermon where three streams join together to form its headwater.
One of the springs used to flow from the mouth of a cave until an earthquake in 1837 caused the cave to collapse. The spring now flows from the base of the cliff in, I believe, much smaller volume.
The area is green and lush with plenty of fresh water and was the site of the city of Caesarea Philippi built about 2 B.C. by Herod Philip, son of Herod the Great and Tetrarch of the area. The fresh water pools, fertile environment, thousand foot elevation & scenic vistas made it one of the most pleasant resorts in Palestine.
However in stark contrast to the pristine surroundings from ancient times the place was the site of worship of pagan nature gods, first Ba'al & then Pan.
Baal
Caesarea Philippi was known as Baal Hermon and Baal Gad in the Old Testament period
from Mount Halak, that rises toward Seir, even as far as Baal-gad in the Valley of Lebanon at the foot of Mount Hermon. And he captured all their kings, and struck them and put them to death. (Joshua 11:17 NASB)
the land of the Gebalites; and all Lebanon to the east, from Baal-gad below Mount Hermon to Lebo-hamath. (Joshua 13:5 BSB)
the five rulers of the Philistines, all the Canaanites, the Sidonians, and the Hivites who lived in the mountains of Lebanon from Mount Baal-hermon to Lebo-hamath. (Judges 3:3 BSB)
Baal was an ancient god worshipped by both the Canaanite and Phoenicians. The name Baal was an ancient Northwest Semitic title meaning "lord" or "owner". In Canaanite and Phoenician mythology, Baal was primarily revered as the storm and fertility god - who eventually claimed the title of king of the gods after defeating rival powers like the sea god Yam and the death god Mot.
The greatest idolatrous apostasy among the Israelites was to the worship of this Phoenician deity, that was fiercely opposed and condemned by many of the prophets. See for example, Elijah's confrontation with the 450 prophets of Baal in 1 Kings 18:21-40
Pan
This site was later named Panias after the Greek god Pan who was worshiped here... However, the name "Banias" (the name that exists today) is an Arabic adaptation of Panias, derived from the ancient Greek god Pan.
In the Hellenistic period, this city was resettled. An open-air sanctuary was built for Pan next to the source of water that exited the cave.... Adjacent to the sacred cave is a rocky escarpment with a series of hewn niches. It is known that statues of the deity were placed in these niches by depictions on coins of the city. One niche housed a sculpture of Echo, the mountain nymph and Pan's consort. Another niche housed a statue of Pan's father, Hermes, son of nymph Maia. Inscriptions in the niches mention those who gave large donations. [11]
Several carved niches still visible in the side of the cliff held statues of the Greek god Pan - the mythical half man, half goat who played the panpipes (also known as Pan Flute or syrinx).
(The Disney character Peter Pan played the pan pipes because J.M. Barrie named his character after the Greek god Pan)
Sacred niches held statues of the Greek god Pan. Courtesy of the Pictorial Library of Bible Lands.
Jesus at Caesarea Philippi
A large part of Jesus' ministry was 20 miles south of this area in the cities of Capernaum, Chorazin and Bethsaida. Shortly before He made His final journey to Jerusalem to be crucified He brought the disciples to Caesarea Philippi, which is not somewhere you get to by accident. In fact, as a practicing Jew, Jesus knew that it was defiling to be in unclean places of idol worship, yet He went out of His way to take the disciples to this specific location. Why?
We read in Matthew 16:13 – 20 that it was at Caesarea Philippi that Jesus probed his disciples perception of him which means that they traveled a long way to go to a pagan temple simply for Jesus to ask the disciples a question He could have asked them anywhere.
Note that in answer to Jesus' question "who do you say I am" Peter said "You are the Christ, the Son of the living God." It is entirely possible that Peter's reference to the "living God" was in contrast to the pagan idols of the area.
The very geography of the place lends credence to the concept that the rock Jesus said He would build His kingdom on was the very rock that they were standing in close proximity to. The rock where the gods Baal and Pan were worshipped.
His next words lend additional credibility to this idea. He said the 'the gates of hell would not prevail against the church'. The traditional and long held view of His words is that the church is like a fortress that the enemy pounds at ... to no avail. However in Old Testament times the gate of the city was its main and foremost defense against the enemy. The city was lost and usually fell quickly if the enemy prevailed against the gates.
The image Jesus painted was exactly the opposite of the conventional belief. He was saying that the church will usurp the power of Satan and his (Satan's) gates will not be able to defend him against the church. The church is the one that does the attacking, not the powers of hell.
In His choosing of this location Jesus was initiating the disciples, preparing them for the work ahead and giving them a broad vision of the mission of the church which is not to hide from the world and hunker down in churches, but to confront the power of the enemy. To challenge the adversary on his own ground. {PLACE IN TEXT}
End Notes
[01] What the Early Church Believed: Apostolic Succession. https://www.catholic.com/tract/apostolic-succession
[02] David Guzik. Study Guide for 2 Timothy 2
https://www.blueletterbible.org/comm/guzik_david/study-guide/2-timothy/2-timothy-2.cfm
[03] David Guzik. Enduring Word. Matthew 16 – Revealing Who Jesus Is and What He Came to Do.
https://enduringword.com/bible-commentary/matthew-16/
[04] Dr. John Ankerberg, and Dr. John Weldon. How Convincing Is the Roman Catholic View That Peter Was the First Pope?
[05] Dave Miller, Ph.D. Are There Modern-Day Apostles?
https://apologeticspress.org/are-there-modern-day-apostles-1226/
[5b] Papal Infallibility. Catholic Answers. https://www.catholic.com/tract/papal-infallibility
[06] Moises Pinedo. Apologetics Press. Was Peter the First Pope?
https://apologeticspress.org/was-peter-the-first-pope-2561/
[07] Kurt Willems. Who was the Apostle Paul? - a brief biography.
https://www.kurtwillems.com/blog/apostle-paul-brief-biography
[08] Bible Pathway Adventures The Power of Roman Citizenship in Ancient Times. https://tinyurl.com/3p97vnun
[09] David Guzik https://enduringword.com/bible-commentary/romans-1/
[10] Was Peter the First Pope? The Bart Ehrman Blog . https://ehrmanblog.org/was-peter-the-first-pope/
[11] Caesarea Philippi. bibleplaces.com. https://www.bibleplaces.com/caesarea-philippi-banias/