Matthew 16:18-19 / Isaiah 22:22
"And I tell you, you are Peter, and on this rock I will build my church, and the powers of death shall not prevail against it. I will give you the keys of the kingdom of heaven, and whatever you bind on earth shall be bound in heaven, and whatever you loose on earth shall be loosed in heaven."
"And I will place on his shoulder the key of the house of David; he shall open, and none shall shut; and he shall shut, and none shall open."
Jesus gives Peter the keys to the kingdom of heaven. While many Protestants think that the gift of the "keys" means that Jesus appointed Peter as the guardian of the gates of heaven, the "keys" actually refer to Peter's authority over the earthly Church (which Jesus often described as the "kingdom of heaven." Matthew 13:24-52; 25:1-2; Mark 4:26-32; Luke 9:27; 13:19-20, etc.) In the Old Davidic kingdom, the king had a prime minister on whose shoulder God placed the keys of the kingdom (Isaiah 22:22). Similarly, the new kingdom of Christ also has a prime minister (Peter and his successors) who is given the keys of the kingdom. The keys not only represent the authority the prime minister has to rule over God's people in the king's absence, but also the means of effecting dynastic succession to the prime minister's office (for example, in Isaiah 22:20-22, Eliakim replaces Shebna as prime minister in the Old Davidic kingdom). Only the Catholic Church claims and proves a succession of prime ministers (popes) all the way back to Peter, and this succession is facilitated by the passing of the keys of the kingdom.
Finally, Jesus declares to Peter that whatever he binds and looses on earth will be bound and loosed in heaven. As in the Old Davidic kingdom, whenever Peter the prime minister opens, no one shall shut, and whenever he shuts, no one shall open. Jesus, therefore, gives Peter the authority to make decisions that will be ratified in eternity. In order for sinful Peter (and his successors through the passing on of the "keys") to make such decisions, he must be divinely protected. Once again, this evidences Jesus' gift of infallibility to the Church. Only the Catholic Church claims and has proven that her 2,000 year-old teachings on faith and morals, which have never changed, are infallibly proclaimed.
Church Fathers:
For it is a matter of necessity that every Church should agree with this Church, on account of its pre- eminent authority, that is, the faithful everywhere, inasmuch as the apostolical tradition has been preserved continuously by those [faithful men] who exist everywhere." Irenaeus, Against Heresies, 3:3:2 (A.D. 180).
"And he says to him again after the resurrection, 'Feed my sheep.' It is on him that he builds the Church, and to him that he entrusts the sheep to feed. And although he assigns a like power to all the apostles, yet he founded a single Chair, thus establishing by his own authority the source and hallmark of the (Church's) oneness. No doubt the others were all that Peter was, but a primacy is given to Peter, and it is (thus) made clear that there is but one flock which is to be fed by all the apostles in common accord. If a man does not hold fast to this oneness of Peter, does he imagine that he still holds the faith? If he deserts the Chair of Peter upon whom the Church was built, has he still confidence that he is in the Church? This unity firmly should we hold and maintain, especially we bishops, presiding in the Church, in order that we may approve the episcopate itself to be the one and undivided." Cyprian, The Unity of the Church, 4-5 (A.D. 251-256).
"You cannot deny that you know that in the city of Rome the Chair was first conferred on Peter, in which the prince of all the Apostles, Peter, satÂ…in which Chair unity should be preserved by all, so that he should now be a schismatic and a sinner who should set up another Chair against that unique one." Optatus of Mileve, The Schism of Donatists, 2:2-3 (c. A.D. 367).