Who really is ‘the Rock’ of Matthew 16?
The Catholic Church maintains a belief that of all the Apostles of Jesus, Peter was the leader. That, because he was in this unique position, the office of Papacy is also the leader of all the churches.
This claim stems in part from Jesus saying “On this rock, I will build my Church”; Catholics assuming that ‘rock’ here refers to the Apostle Peter himself. And as a result of this, Peter’s successors are to inherit some special power over the whole church. But what in fact did the early church make of this statement?
A survey of early church fathers commentaries shows seventeen Fathers thought of the rock as Peter, forty-four thought it referred to Peter’s confession of faith, sixteen thought Christ Himself was the rock, while eight thought that the rock meant all of the Apostles. Thus 80% of these Church Fathers did not recognize ‘the rock’ as meaning Peter alone. Such a claim of papal commission therefore is not so clear-cut.
One Father, Augustine of Hippo wrote “See what praises follow this faith. ‘Thou art Peter, and upon this rock I will build this Church. What meaneth, ’Upon this rock I will build My Church’? Upon this faith; upon this that has been said, ‘Thou art the Christ the Son of the Living God. Upon this rock,’ saith He, ‘I will build My Church” (Homily X on John V. 1-3).
St. Cyprian stated “Faith is the foundation of the Church, for it was not of the person but of the faith of St. Peter that it was said that the gates of hell should not prevail against it; it is the confession of faith that has vanquished hell. Jesus Christ is the Rock. He did not deny the grace of His name when He called him Peter, because he borrowed from the rock the constancy and solidity of his faith. Endeavour then, thyself to be a rock ‘thy rock is thy faith, and faith is the foundation of the Church. If thou art a rock, thou shalt be in the Church for the Church is built upon the rock.” (De Catholicae Ecclesia Unitate, cap. 4-5).
Turning again to Augustine: “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 saith, ‘Thou art
Peter; and upon this Rock’ which thou hast confessed, upon this Rock which
thou hast acknowledged saying, ‘Thou art 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 thee upon Myself, not Myself
upon thee. For men who wish to be built upon men, said, ‘I am of Paul: and
I of Appollos; and I of Cephas,’ (1Cor. 1:12) who is Peter, but upon the
Rock, said ‘But I am of Christ.
“And when the Apostle Paul ascertained that he was chosen, and Christ despised, he said, ‘Is Christ divided’? Was Paul crucified for you? Or were ye baptized in the name of Paul’? (1Cor 1:13) And, as not in the name of Paul, so neither in the name of Peter; but in the name of Christ: that
Peter might be built upon the Rock, not the Rock upon Peter.”
(Sermon XXVI Matt. XIV, 25).
Thus, St. Cyprian says ”For neither did Peter, whom first the Lord chose, when Paul disputed with him afterwards about the circumcision, claim anything to himself insolently, nor arrogantly assume anything, so as to say that he held
primacy, and that he out to be obeyed to novices and those lately come.”
(Epistle LXX concerning the baptism of Heretics). 
Another claim deals with the belief that the power of loosing and binding was given to Peter alone. However Matthew 18:18 shows that all the Apostles received the same powers. Thus to turn to St. Augustine once more.
“He had not the primacy over the disciples (in discipulos) but among the disciples (in disipulis). His primacy among the disciples was the same as that of Stephen
among the deacons.” (Sermon 10 on Peter and Paul).
 Jean de Launoy Epist. Vii., Opp. Vol. V., pt 2. p.99, Geneva, 1731 quoted in Whelton, M., (1998 ), “Two Paths: Papal Monarchy : Collegial Tradition”, p27. On the issue of ‘the Rock’ and ‘the Keys’ we can look to other great thinkers… (see also Appendix A) to determine how they interpreted these words. Also
 Ibid, pp27-8. also at ccel.org/fathers2/NPNF1-07/npnf1-07-141.htm#P4618_2490251
 Ibid, p28. Note that St. Cyprian re-occurs a number of times as one of the so-called ‘champions’ of Papal Primacy – we shall visit him again as well.
 Ibid, pp31-32 quoted also at ccel.org/fathers2/NPNF1-06/npnf1-06-43.htm#P4186_1789723
 Whelton, p34.
 Ibid, p-33.