I picture Jesus holding a larger rock in one hand and a smaller rock in the other and saying to Peter he is the latter, and the Lord is the former, and the Church is built on this larger rock. He says this right after saying, "for flesh and blood hath not revealed it unto thee, but my Father which is in heaven" (Matt. 16.17). What was revealed? That Jesus "art the Christ, the Son of the living God" (v.16). So naturally the Church is built on the One being spoken of. Then Jesus says, "I will give unto thee the keys of the kingdom of heaven" (v.19). He doesn't give him the key to the Church but to the kingdom of heaven. If Jesus gave Peter the keys to the Church, Roman Catholicism might be true, but Jesus makes no mistake here.

Is. 9.6 says Jesus is the "Everlasting Father". This is not to say He is the 1st Person of the Trinity but that Jesus is the chief as it were.

While petros is used in different instances, the context surrounding Jesus' talk with Peter is that of two rocks, one smaller and one larger, to bring home a point.