One evening, I was going to a mid-week service at my home church. Everything was going rather well, we were discussing Jesus as a child impressing the church leaders. To my surprise, out of nowhere, this baptist teacher says (paraphrasing) “We know Peter is the first pope, so…” I can’t remember where he was going with it, probably because I was shocked to hear a protestant say such a thing.
“Peter the first pope, don’t you realize you’re giving them too much credit?” I reasoned to myself.
Now, don’t get me wrong, even if Peter was a pope of any sorts, I don’t think it necessarily follows that therefore Roman Catholicism is true, but it does give weight to their arguments.
It blindsided me because the history of the Popes is not exactly easy to pin down. There is a lot of ambiguity surrounding the history of the Popes. From Honorius, stories of gossip, orgies, and drug use, Popes have been very controversial. (Look up Pope Leo XIII) It isn’t an easy “Yes, he was pope” or “No he wasn’t” however, I intend to prove that he was probably not a pope.
And I say also unto thee, That thou art Peter, and upon this rock I will build my church; and the gates of hell shall not prevail against it. (Matthew 16:18 KJV)
Matthew 16:18 is the go-to verse for your average everyday Catholic when asked about Peter being the first pope. However, it is a tough sell. Several issues arise such as:
The Church Fathers not being anywhere close to unanimous on the interpretation of this verse. Some saying the rock was Peter, Peter’s confession, or Christ himself.
Hilary of Poitiers, a doctor of the church states:
“Upon this rock of the confession is the building up of the church. This faith is the foundation of the church. Through this faith the gates of hell are powerlessagainst it. This faith hath the keys of the heavenly kingdom.” 
Christ is the rock, who granted to Hisapostles that they should be called rocks.”(commenting on Amos 6:12) “But thou says that church is founded on Peter, albeit the very same thing is also done upon all of the apostles, and they all receive the keys of the kingdom of heaven, and the strength of the church is established on them all equally.” John Chrysostom said:
“‘I say unto thee, Thou are Peter, and upon this rock, will I build My church;’ that is, on the faith of his confession.” 
‘Thou art Peter, and upon this rock I will build My church,’ that it should be understood as upon Him whom Peter confessed, saying, ‘Thou art the Christ, the Son of the living God,’ and that Peter, named from this rock, represented the person of the church, which is built on the rock, and received the keys of the kingdom of heaven. For it was not said to him, ‘Thou are the rock’ (petra), but, ‘Thou art Peter (petros). For Christ was the rock whom Simon confessing, as the whole church confesses Him.” 
There are many more, but I will not make this post a novel and spare you the reading of so many quotes in a row.
It also tries to prove too much. Even if the rock is referring to Peter, it does not necessarily follow with the packaged deal of a papacy. Let me humor this point of view for a moment.
Peter is the rock, Christ shall build the church on Peter, because Peter is an apostle who will go on to write new testament epistles and spread the gospel, therefore building the church.
That explanation is just as logically valid as the pope inference. Even if Peter is the so-called chief of the apostles, it would only follow that he was a leader, not that he was a papal leader. So the Catholic would need to provide more than just this verse to establish Peter as the first pope.
Peter throughout the new testament is never treated like a pope, nor does he issue commands like one. This is not me comparing Peter to Pope Francis, as I understand the Roman Catholic Church has changed quite a bit over the years.
There is also a major gap in the historical records, for we cannot even prove Peter spent a significant time in Rome. In fact, no reference was made about a bishop of Rome until the late second century/early third century.
Here is quote within a quote, quoteception
The claim of Peter living in Rome, however briefly, and being martyred there is thus a second-century creation designed to address the political needs of the Roman church. The legend came to be accepted as an unquestioned statement of faith by the time of Eusebius in the fourth century and by all church historians thereafter.Pheme Perkins, a Boston College professor and a Roman Catholic, made the following summary in her award-winning book, Peter: Apostle for the Whole Church:
“Since we have no evidence of when Peter arrived in Rome or the circumstances that led to his execution, later claims that he was bishop in a Roman community must rest on traditions about the apostle which emerged in the second century. For the first century of its existence, there was probably not a single bishop in the Roman church.”
Perkins opines that Anicetus (ca. 154–165 C.E.) was probably the first bishop over the entire church at Rome, whereas others listed before him oversaw individual house churches—small groups meeting in people’s homes.
Catholic scholar H. Burn-Murdoch states
“None of the writings of the first two centuries describe Peter as a bishop of Rome 
Protestant Theologian Herman Bavinck states:
“It is clear from the bishops’ lists in Hegesippus, Irenaeus, the Muratorian Fragment, Hippolytus, Tertullian, and Epiphanius that at the end of the second century and even in the beginning of the third, Peter was not yet considered a bishop of Rome”
Catholic Scholars Raymond Brown and John Meier state
Indeed, the signal failure of Ignatius (ca. 110) to mention the single-bishop in his letter to the Romans (a very prominent theme in his other letters) and the usage of Hermas, which speaks of plural presbyters (Vis. 2.4.2) and bishops (Sim. 9.27.2), make it likely that the single-bishop structure did not come to Rome till ca. 140-150” 
Meier states elsewhere
As we have seen from 1 Clement, at the end of the first century, the Roman church was governed by presbyter-bishops assisted by deacons. At the end of the second century, single bishops like Victor I seem firmly in control” 
Van Engen points out
“Singular emphasis upon Peter as the founder and first bishop of Rome first emerged in the third century and became prominent in the late fourth century”
The Council of Chalcedon stated:
“In all respects following the definitions of the holy Fathers, and acknowledging the canon of the 150 God-beloved bishops which has just been read, we likewise make the same definition and decree concerning the precedence of the most holy church of Constantinople, or new Rome. For the Fathers with good reason bestowed precedence on the chair of old Rome, because it was the imperial city, and the 150 God-beloved bishops, moved by the same view, confer equal precedence on the most holy throne of new Rome, rightly judging that the city honored with the empire and the senate should enjoy the same precedence as Rome, the old seat of empire, and should be magnified as it was in ecclesiastical matters also, being second after it.”
Jesse C. Stevens brings up an excellent point in his paper “Was Peter the First Pope?”
“Thus in a general council, Constantinople is placed on a level with Rome, and that in the latter part of the fifth century; and every reader of history knows that this rivalry continued between Rome and
Constantinople (it began a long time before this council) until Justinian, in the year 533 AD, decreed that the bishop of Rome should be the head of the universal church.”
Keith Thompson of Reformed Apologetic Ministries rightly points out two important things. The first being that Church Fathers who could have easily added the information that Peter was the first pope simply didn’t. This would be like a Catholic Apologist today not mentioning Pope Francis in any of their writings. Imagine a politician or political analyst today never mentioning President Trump!
“…While Tertullian (A. D. 160-225) affirmed Peter and Paul gave the gospel to Romans (Tertullian, Against Marcion, 4.5), that Peter ordained Clement as the first bishop of Rome (Tertullian, Demurrer Against the Heretics, 32.1), and that Peter taught there at times and died there (Tertullian,Demurrer Against the Heretics, 36.1), he never said Peter was Rome’s first bishop. This is astonishing in light of Romanism’s claim to historicity…It is sometimes falsely claimed that Hippolytus (A.D. 170-225) named Peter as the first bishop of Rome in the Liberian Catalog which lists alleged bishops of Rome starting with Peter and ending with Liberius. However, this list actually comes from A.D. 354 as even Catholic scholar Philippe Levillain admits: “Shortly after Eusebius, however, in AD 354, an unknown complier prepared a list of Roman bishops which differs significantly from Eusebius’s. This list, usually called the ‘Liberian Catalogue’ since Liberius is the last mentioned Roman bishop” (Philippe Levillain The Papacy: An Encyclopedia, Volume 2, [Routledge, 2002], p. 1064; see also Thomas J. Herron, Clement and the Early Church of Rome, [Emmaus Road Publishing, 2010], p. 97). It is speculated by certain Catholics that Hippolytus may have authored portions of the list earlier but to dogmatically claim he is the one who named Peter as being the first Roman bishop is just not demonstrable…” 
Lastly, Leo the Great (440-461 A.D.) was the first to claim to be Peter’s heir
Peter as the first pope is based on an inference on one text that isn’t agreed upon by the Church Fathers with no real historical backing. However, even if the Catholics are right about the verse, it doesn’t prove what they claim.
There is no first-century historical evidence for Peter ever being the bishop in Rome and it is based on political second-century writings that were made, in which that type and style would be common for myth-making.
Because of the exegetical uncertainty and lack of historical evidence, Peter was probably not the first pope.
 The Church Father’s Interpretation of Matthew 16:18 by William Webster
 On the Trinity 6:36-37, Hilary of Poitiers
 Jerome Adv. Jovin ii. cited in The Petrine Claims: A Critical Inquiry by Richard Frederick Littledale  John Chrysostom, (comments on Matthew 16:13, paragraph 3, Homily 54)
 Augustine: The Retractions, Retraction 1:21
 The Birth of a Legend at Vision.org
 H. Burn-Murdoch, The Development of the Papacy, [Faber & Faber, 1954], p. 130).
 Herman Bavinck, Reformed Dogmatics, Vol. 4, trans. John Vriend, ed., John Bolt, [Baker Academic, 2008], p. 365
 Raymond Brown, John P. Meier, Antioch and Rome, [Paulist Press, 1983], p. 204).
 John P. Meier, The Petrine Ministry in the New Testament and the Patristic Traditions, ed., J. F. Puglisi, How Can the Petrine Ministry Be a Service to the Unity of the Universal Church?, [Wm. B. Eerdmans Publishing, 2010], p. 28)
 J. Van Engen, “Primacy of Peter,” ed. Walter A. Elwell, Evangelical Dictionary of Theology, [Baker Academic, 2001], p. 910
 The Council of Chalcedon, 451 A.D.
 Was Peter the First Pope? by Jesse C. Stevens (pdf)
 Reformed Apologetics Ministries: Absence of Papal Views Among Earliest Christians by Keith Thompson
 Pope Leo historical profile at the Church History Institute