CATECHISM OF THE CATHOLIC CHURCH
424. "Moved by the grace of the Holy Spirit and drawn by the Father, we believe in Jesus and confess: 'You are the Christ, the Son of the living God.'[Mt 16:16 .] On the rock of this faith confessed by St. Peter, Christ built his Church.[Cf. Mt 16:18; St. Leo the Great, Sermo 4 3: PL 54,150 - 152; 51,1: PL 54, 309B; 62, 2: PL 54, 350-351; 83, 3: PL 54, 431-432.] 'To preach. . . the unsearchable riches of Christ'[Eph 3:8.]"
552. "Simon Peter holds the first place in the college of the Twelve;[Cf Mk 3:16 ; Mk 9:2; Lk 24:34 ; 1 Cor 15:5.] 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.'[Mt 16:18 .] Christ, the 'living Stone',[1 Pet 2:4.] 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.[Cf. Lk 22:32 .]"
According to the CCC (Infallible-Yes?) the Church was built on the rock of the faith confessed by Peter never upon Peter himself.
Oh, and "universal" is small "c" catholic.
But, but, but, but......
That’s NOT what the Catholic church “really” teaches, dontcha know?
And just to provide a source so that no one can accuse you of making that up, here’s the vatican.va link.
http://www.vatican.va/archive/catechism/p1s2c2.htm
424 Moved by the grace of the Holy Spirit and drawn by the Father, we believe in Jesus and confess: ‘You are the Christ, the Son of the living God.’8 On the rock of this faith confessed by St. Peter, Christ built his Church.9
Good work....