I assume a certain level of scriptural literacy, as well as English grammar, and so, perhaps, am more terse in my comments than you require. Try reading in your Bible both before and after the portion the Catechism quotes. Messiah blessed Simon. Messiah called Simon by the name Peter, a Greek rendition of the Aramaic name, Cephas, He already gave Simon much earlier, and promised to build His church on this rock. Messiah promises to give Peter the keys to the kingdom of heaven and the power to bind and loose. At least you are reading the Catechism of the Catholic Church. I hope that you can benefit as it is do very well written. At least it will not harm you, and if you can trade cynicism for love you shall prosper indeed.
Let me recommend this portion and see if the answer to your awkward question comes to you.
552 Simon Peter holds the first place in the college of the Twelve;283 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."284 Christ, the "living Stone",285 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.286
No, the UNSHAKABLE rock is Jesus Christ - always was always will be. When St. Peter died a martyr's death in 64 A.D. that "first place" of leadership did as well. You have NOTHING in Scripture that proves Peter's leadership among the Apostles and the local assemblies he helped to form was, or could be, passed on from Peter to someone else. Your religion takes a huge logic leap - unfounded within the writings of even the early church leaders - by saying this "primacy" was something that could be handed down for thousands of years and was what Jesus meant by saying to Peter what He did.
As has been shown at least a dozen times on this thread alone, there was no Pope Peter, head over all Christendom, there was no Pope of Rome nor a succession of Popes of Rome that led all of Christendom, there was no head bishop that all Christendom had to obey. There was no church called the Roman Catholic Church until at least four centuries after the last Apostle died. The very word "catholic" wasn't even used until the second century and then only as an adjective describing the "universal" body of believers in Christ. All that Roman Catholicism teaches today about Apostolic Succession is something they invented and developed over time. They didn't get it from Christ, they didn't get it from Peter.
You can spin all day. The Rock is Jesus. Never was and never will be on a fallible human. You go right ahead and put your trust in fallible man. True followers of Christ put their trust in Him alone. Those who God is truly calling will never put a fallible human between themselves and God.