Peter was not the first pope. Peter’s characteristics are not the characteristics of a pope and the Bible does not say he was a pope.
Unlike popes of this day, Peter was married. Matthew 8:14 speaks of Peter’s mother-in-law and I Corinthians 9:5 also says Peter had a wife.
Peter’s spiritual judgment was not infallible. Paul “said to Cephas in the presence of all, ‘if you being a Jew, live like the Gentiles and not like the Jews, how is it that you compel the Gentiles to live like Jews?’” (Galatians 2:14) Matthew 16:21-23 also says Peter’s spiritual judgment was not true. “From that time Jesus Christ began to show His disciples that He must go to Jerusalem, and suffer many things from the elders and chief priests and scribes, and be killed, and be raised up on the third day. And Peter took Him aside and began to rebuke Him, saying, ‘God forbid it, Lord! This shall never happen to you.’”
Popes are supposed to not marry and not make spiritual mistakes. Thus Peter could not be the first pope.
Let us look at the verse Roman Catholics use to say Peter was the first pope. What does it really mean? The verse is Matthew 16:15-18 saying, “He said to them, ‘But who do you say that I am?’ And Simon Peter answered and said, ‘Thou art the Christ, the Son of the living God.’ And Jesus answered and said to him, ‘Blessed are you, Simon Barjona, because flesh and blood did not reveal this to you, but My Father who is in heaven, and I also say to you that you are Peter, and upon this rock I will build My church.’”
It should be noted that Peter means in Greek a small stone while rock means in Greek a large rock. They are different words. Thus the church was not built on Peter: it was built on Peter’s reply, “Thou art the Christ, the Son of the living God.”
We see from all this Peter was not the first pope. The words papacy, pope, and pontiff are not in the Bible. The characteristics of Peter are not the characteristics of a pope. Lastly the church was not built on Peter, but on his words, “Thou art the Christ the Son of the Living God.” (Matthew 16:15-18)
Quotations from the NASB Bible.