"When Jesus came into the coasts of Caesarea Philippi, he asked his disciples, saying, Whom do men say that I the Son of man am? And they said, Some [say that thou art] John the Baptist: some, Elias; and others, Jeremias, or one of the prophets. He saith unto them, But whom say ye that I am? And Simon Peter answered and said, Thou art the Christ, the Son of the living God. And Jesus answered and said unto him, Blessed art thou, Simon Barjona: for flesh and blood hath not revealed [it] unto thee, but my Father which is in heaven. 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. And I will give unto thee the keys of the kingdom of heaven: and whatsoever thou shalt bind on earth shall be bound in heaven: and whatsoever thou shalt loose on earth shall be loosed in heaven. Then charged he his disciples that they should tell no man that he was Jesus the Christ." - Matthew 16:13-20
Throughout the Acts of the Apostles, St. Peter is clearly the leader of the Christian community (Acts 1:15, 5:1-10). And again, he is listed first among the Apostles in the New Testament (Matthew 10:2; Mark 3:16-19; Luke 6:13-14). Before St. Peter was crucified, he appointed St. Linus as his successor. Why should this practice not be carried on to the present day? There is an unbroken line of Popes from St. Peter down to the present-day Pope. The Papacy is the oldest institution in the Western World. How could it have survived 2000 years without the grace of God and the guidance of the Holy Spirit?
St. Hegessipus in the 2nd century of the Church had already compiled a list of the popes, listing the current one at the time (Pope Anacletus) as the eleventh successor to St. Peter.
Acts 1:15? Peter spoke. That's amazing! Not impressed again.
Try Galatians 2:2,6
2 I went up because of a revelation and set before them (though privately before those who seemed influential) the gospel that I proclaim among the Gentiles, in order to make sure I was not running or had not run in vain.
6 And from those who seemed to be influential (what they were makes no difference to me; God shows no partiality)--those, I say, who seemed influential added nothing to me.
So Paul did not submit to Peter? Paul says that God shows no partiality. I know you'll ignore this, but God doesn't show partiality to Peter. That's Scriptural. Peter appointing Lunis as pope? Not Scriptural.
And then in 1 Corinthians
4 For when one says, "I follow Paul," and another, "I follow Apollos," are you not being merely human?
5 What then is Apollos? What is Paul? Servants through whom you believed, as the Lord assigned to each.
6 I planted, Apollos watered, but God gave the growth.
7 So neither he who plants nor he who waters is anything, but only God who gives the growth.
8 He who plants and he who waters are one, and each will receive his wages according to his labor.
It's all about God. Not individual men.
And historically...
When there had for a along time been disputes between the bishop of Rome and Constantinople over the primacy, Emperor Phocas had finally decided that the primacy should be assigned to the bishop of Rome. But if the ancient church had acknowledged the primacy of the Roman pontiff, this dispute could not have occurred, nor would a decree of the emperor have been necesarry.