You mean, the rock is really the faith of Peter, not Peter as a person. This is a possible, even patristic interpretation of the episode. However, let us not look at the renaming alone. St. Peter is also given the keys to the Kingdom of Heaven and the power to bind and loose, later given the rest of the Apostles. His weaknesses Christ saw, right in the keys episode and another time at the Last Supper. But after Peter's betrayal the charge to feed the sheep is repeated three times; at the Last Supper Christ prays for Peter personally and asks him to convert his brethren. Which he does, as we read in Acts. Taken together, these scriptures do not allow any trivilaization of the renaming episode, and instead place it on the same level as the other epochal renamings in the Old Testament, of Abram and of Jacob.
Not true.. The keys were given to the church corporately not Peter.. to all the rocks/stones not just one stone.. The Holy Spirit is the ONLY authority in the church.. not Peter.. or by the way Mary..
Unless you believe that Jesus did not know the future of the church at that time(with Peter).. Suggest you read the revelation of Jesus Christ(revelation ch 1;1)... Because that book is the Revelation of Jesus Christ not John the Apostle who transcribed it.. All Christian church organizations on this planet are clubs.. including Protestant ones.. The Roman Catholic church is merely a club.. Some of those clubs do have members of the church.. with some of them officers in a club..
The keys are really considered to have been given the church.
Granted whether the rock is Peter or his faith changes that as well.
If one accepts that it's Peter's faith which is the rock, then the church which has maintained that faith is the rightful 'heir' or successor to holding the keys.
If one thinks it's tied to Peter's office it's still questionable seeing as Peter founded more than one church, and frankly more than one ancient see. That said the church fathers do indicate which See has primacy over the rest.
(Though I'd question exactly what that primacy entails, and whether that primacy is due to the keys being 'inherited by' that see alone).