Personally, I think the ideas expressed in the second line of CCC paragraph
424 could have been phrased better, and in fact were in paragraph 552:
552 Simon Peter holds the first place in the college of the Twelve; Jesus entrusted a unique mission to him. Through a revelation from the Father, Peter had confessed: “You are the Christ, the Son of the living God.” Our Lord then declared to him: “You are Peter, and on this rock I will build my Church, and the gates of Hades will not prevail against it.” Christ, the “living Stone”, thus assures his Church, built on Peter, of victory over the powers of death. Because of the faith he confessed Peter will remain the unshakable rock of the Church. His mission will be to keep this faith from every lapse and to strengthen his brothers in it.
It is made very clear here that
Peter is the rock and was made the rock **because of **his great faith. Additionally, paragraph 881 states:
881 The Lord made Simon alone, whom he named Peter, the “rock” of his Church. He gave him the keys of his Church and instituted him shepherd of the whole flock. “The office of binding and loosing which was given to Peter was also assigned to the college of apostles united to its head.” This pastoral office of Peter and the other apostles belongs to the Church’s very foundation and is continued by the bishops under the primacy of the Pope.
Notice also footnote 9 to the phrase in question in paragraph 424. It references several excerpts from the Sermons of Pope St. Leo the Great, one of Peter’s greatest successors. We read in one of these (
Sermon 51):
To strengthen, therefore, their most wholesome knowledge of this belief, the Lord had asked His disciples, among the various opinions of others, what they themselves believed, or thought about Him: whereat the Apostle Peter, by the revelation of the most High Father passing beyond things corporeal and surmounting things human by the eyes of his mind, saw Him to be Son of the living God, and acknowledged the glory of the Godhead, because he looked not at the substance of His flesh and blood alone;
and with this lofty faith Christ was so well pleased that he received the fulness of blessing, and was endued with the holy firmness of the inviolable Rock on which the Church should be built and conquer the gates of hell and the laws of death, so that, in loosing or binding the petitions of any whatsoever, only that should be ratified in heaven which had been settled by the judgment of Peter.