"Peter was not the Rock upon which Christ was to build His church. Peter's confession was."
This is the position of Orthodoxy and indeed even of several of the particular churches which are in communion with the Bishop of Rome. This is not to say that Orthodoxy does not recognize that, all things theological being equal, the Bishop of Rome is not the first among the equal bishops of The Church as +Peter was among the apostles.
Why would Orthodoxy think that about Rome? Real question.
I don't have a big argument against it. My point is, these are interpretations. The text does not contain them. There is surely nothing in the text to separate the person of St. Peter from the disembodies confession, as the renaming cannot be done to a confession, but perhaps to the man confessing.