MATTHEW 16 13 When Jesus came into the region of Caesarea Philippi, He asked His disciples, saying, “Who do men say that I, the Son of Man, am?”14 So they said, “Some say John the Baptist, some Elijah, and others Jeremiah or one of the prophets.”15 He said to them, “But who do you say that I am?”16 Simon Peter answered and said, “You are the Christ, the Son of the living God.”17 Jesus answered and said to him, “Blessed are you, Simon Bar-Jonah, for flesh and blood has not revealed this to you, but My Father who is in heaven. 18 And I also say to you that you are Peter, and on this rock I will build My church, and the gates of Hades shall not prevail against it. 19 And I will give you the keys of the kingdom of heaven, and whatever you bind on earth will be bound in heaven, and whatever you loose on earth will be loosed in heaven.”20 Then He commanded His disciples that they should tell no one that He was Jesus the Christ.

This is not the property of Peter alone, but it came about on behalf of every human being. Having said that his confession is a rock, he stated that upon this rock I will build my church. This means he will build his church upon this same confession and faith. For this reason, addressing the one who first confessed him with this title, on account of his confession he applied to him this authority, too, as something that would become his, speaking of the common and special good of the church as pertaining to him alone. It was from this confession, which was going to become the common property of all believers, that he bestowed upon him this name, the rock.
(Theodore of Mopuestia)