1 The Gospel which has just been read touching the Lord Christ, who walked on the waters of the sea; and the Apostle Peter, who as he was walking, tottered through fear, and sinking in distrust, rose again by confession, gives us to understand that the sea is the present world, and the Apostle Peter the type of the One Church. For Peter in the order of Apostles first, and in the love of Christ most forward, answers oftentimes alone for all the rest. Again, when the Lord Jesus Christ asked, whom men said that He was, and when the disciples gave the various opinions of men, and the Lord asked again and said, “But whom say ye that I am?”
Peter answered, “You are the Christ, the Son of the living God.” One for many gave the answer, Unity in many. Then said the Lord to Him, “Blessed are you, Simon Barjonas: for flesh and blood has not revealed it unto you, but My Father which is in heaven.” Then He added, “and I say unto you.” As if He had said, “Because you have said unto Me, 'You are the Christ the Son of the living God;' I also say unto you, 'You are Peter.'” For before he was called Simon. Now this name of Peter was given him by the Lord, and that in a figure, that he should signify the Church.
For seeing that Christ is the rock (Petra), Peter is the Christian people. For the rock (Petra) is the original name. Therefore Peter is so called from the rock; not the rock from Peter; as Christ is not called Christ from the Christian, but the Christian from Christ. “Therefore,” he says, “You are Peter; and upon this Rock” which you have confessed, upon this Rock which you have acknowledged, saying, “You are the Christ, the Son of the living God, will I build My Church;” that is upon Myself, the Son of the living God, “will I build My Church.” I will build you upon Myself, not Myself upon you.
Source: Sermons on Selected Lessons of the New Testament (New Advent)