-A8
So does the Church act in blessed hope through this troublous life; and this Church symbolized in its generality, was personified in the Apostle Peter, on account of the primacy of his apostleship. For, as regards his proper personality, he was by nature one man, by grace one Christian, by still more abounding grace one, and yet also, the first apostle; but when it was said to him, "I will give unto thee the keys of the kingdom of heaven, and whatsoever you shall bind on earth, shall be bound in heaven; and whatsoever you shall loose on earth, shall be loosed in heaven," he represented the universal Church, which in this world is shaken by divers temptations, that come upon it like torrents of rain, floods and tempests, and falls not, because it is founded upon a rock (petra), from which Peter received his name. For petra (rock) is not derived from Peter, but Peter from petra; just as Christ is not called so from the Christian, but the Christian from Christ. For on this very account the Lord said, "On this rock will I build my Church," because Peter had said, "Thou art the Christ, the Son of the living God." Matthew 16:16-19 On this rock, therefore, He said, which you have confessed, I will build my Church. For the Rock (Petra) was Christ; 1 Corinthians 10:4 and on this foundation was Peter himself also built. For other foundation can no man lay than that is laid, which is Christ Jesus. 1 Corinthians 3:11 The Church, therefore, which is founded in Christ received from Him the keys of the kingdom of heaven in the person of Peter, that is to say, the power of binding and loosing sins. For what the Church is essentially in Christ, such representatively is Peter in the rock (petra); and in this representation Christ is to be understood as the Rock, Peter as the Church. This Church, accordingly, which Peter represented, so long as it lives amidst evil, by loving and following Christ is delivered from evil. But its following is the closer in those who contend even unto death for the truth . . . . For the whole body of the saints, therefore, inseparably belonging to the body of Christ, and for their safe pilotage through the present tempestuous life, did Peter, the first of the apostles, receive the keys of the kingdom of heaven for the binding and loosing of sins; and for the same congregation of saints, in reference to the perfect repose in the bosom of that mysterious life to come did the evangelist John recline on the breast of Christ. For it is not the former alone but the whole Church, that binds and looses sins; nor did the latter alone drink at the fountain of the Lord's breast, to emit again in preaching, of the Word in the beginning, God with God, and those other sublime truths regarding the divinity of Christ, and the Trinity and Unity of the whole Godhead. which are to be yet beheld in that kingdom face to face, but meanwhile till the Lord's coming are only to be seen in a mirror and in a riddle; but the Lord has Himself diffused this very gospel through the whole world, that every one of His own may drink thereat according to his own individual capacity.
Peter as a symbol of the church I can buy, because 2 chapters later Christ gives the power of binding and loosing to much more than just Peter. Peter's primacy is in the office of apostle, not in himself. Peter wasn't made the head of the church, but as an apostle played a very special role in the foundation of the church. Finally, Augustine here is not referring to Peter as the Rock to which Christ as referring. Yes, Peter is A Rock, but re-read it and see Augustine shows that it is Peter's CONFESSION that is the Rock that Christ, THE TRUE ROCK, will build his church upon.