Dare I put this on the table:

"There [John 6:68–69] speaks Peter, upon whom the Church would be built, teaching in the name of the Church and showing that even if a stubborn and proud multitude withdraws because it does not wish to obey, yet the Church does not withdraw from Christ. The people joined to the priest and the flock clinging to their shepherd are the Church. You ought to know, then, that the bishop is in the Church and the Church in the bishop, and if someone is not with the bishop, he is not in the Church. They vainly flatter themselves who creep up, not having peace with the priests of God, believing that they are
secretly [i.e., invisibly] in communion with certain individuals. For the Church, which is one and Catholic, is not split nor divided, but it is indeed united and joined by the cement of priests who adhere one to another" (ibid., 66[69]:8).

&

"There is one God and one Christ, and one Church, and one chair founded on Peter by the word of the Lord. It is not possible to set up another altar or for there to be another priesthood besides that one altar and that one priesthood. Whoever has gathered elsewhere is scattering" (Letters 43[40]:5 [A.D. 253]).

Just some food for thought about "The one chair founded on Peter by the word of the Lord."

Peter the Rock, Peter the fisherman, Peter the man who was given a task by the good man himself, our Lord JC.