The Catholic church claims that their roots began when Yeshua (Jesus) appointed Peter as the first Pope, based on Matthew 16:18: "And I tell you, you are Peter, and on this rock I will build my church, and the power of death shall not prevail against it."
Protestants will tell you that the rock is not Peter, but Jesus himself, as shown in 1 Corinthians 10:4: “And did all drink the same spiritual drink: for they drank of that spiritual Rock that followed them: and that Rock was Christ.” You can go back to the Old Testament, to Deuteronomy 32:15, and see the phrase “Rock of his salvation”, where the word “salvation” is the word Y’Shua, the Hebrew name for Jesus. They interpret the verse in Matthew as, “You are Peter, but on myself, the rock, will I build my church.” The Catholics reject this, and point to the Greek play on words, "You are Petros (Peter) and on this Petra (rock) I will build…", as if the presence of a word play is enough to confirm their interpretation.
It is interesting to note that many Bible scholars, in light of the discovery of the Dead Sea Scrolls, are convinced that the New Testament, like the Old Testament, was originally written in Hebrew. In the Hebrew rendering of this verse, there is also a word play, which is a very common Hebrew writing style, much more common than it is in Greek. The Hebrew version of this verse says to Peter that “you are a stone (which is the Hebrew word spelled aleph, bet, nun - pronounced “aben”), and I will build (which is the Hebrew word spelled aleph, bet, nun, hey - pronounced “abenah”) my house upon a rock.” Had I written this verse, I would have called Peter a pebble and Yeshua a boulder, if I were using stones and rocks to describe them. But the point is that there is a word play in both languages, so the presence of a word play is not enough to form a conclusion.
Another reason that casts significant doubt on the idea that Peter was the first pope is that there is no other verse in the New Testament that lends any support to Peter having been the head of the church. Rather, there are many instances that show that he was not the head of the church. This is not to say that Peter did not play an important role in the early church, because clearly he did. But scripture never says that he was the head of the church. You should always beware of any doctrine that is built on only a single verse.
Here is what the whole of Scripture teaches. When you look at the council of Jerusalem found in Acts 15, James was the presiding officer in charge. When decisions were made on where the missionaries would travel, it was determined by “the apostles” (see Acts 8:14, where “the apostles” sent Peter and John to Samaria.) Had Peter been “the pope”, would “the apostles” be telling him where to go? We also see the church, or the apostles and elders, directing where other missionaries would travel, as with Barnabas in Acts 11:22, and Judas and Silas in Acts 15:22-27. Why would “the apostles” have such authority if Peter alone was the head of the church?
A great deal of the New Testament consists of Paul’s letters to the Gentile churches. Several hints about Peter’s roles can be found here. In Galatians 2:7-15, we are told that Peter was preaching to the Jews, while Paul was preaching to the gentiles. Had Peter been the Pope, he would have been overseeing everything, not just preaching to Jews, as shown in verse seven. One of the most telling verses is verse nine, where Paul names the “pillars” of the church as “James, Cephas (Peter), and John”. Would Paul have dared to name three pillars, with “the pope” in second position? Additionally, beginning in verse 11, Paul admonished Peter for his hypocrisy in removing himself from the gentiles in the presence of Jews. Had Paul and the others present considered Peter as the pope (the supposed infallible head of the church) they would never have dared to rebuke him publicly. 1 Corinthians 1:12-13 also shows that there were a number of church leaders on even footing with Peter in the eyes of the converts. There were contentions among some of the Corinthians based on who had baptized or converted them. “Now this I say, that every one of you saith, I am of Paul and I of Apollos; and I of Cephas; and I of Christ.” Had Cephas (Peter) been the pope, surely the new believers would have been taught this and not had any divisions among themselves based on who was their leader.
As you can see, there is plenty of evidence in Scripture to refute the idea that Peter was appointed pope by Yeshua, which of course then calls into doubt the whole idea that any church is the only true church based on their claim to be direct from the lineage of Peter. A better way to determine the true church of God is to find a body of believers who reflect the Messiah in every way, which sadly does not seem to describe any organized Christian church today, all of which are steeped in varying degrees of paganism and have lost sight of much precious Biblical truth.