All of it.
It rides and falls on the contention that "Peter and his successors" have a connection that allows them to be the final say no matter what. Doctrinal development, custom, everything is attached to this claim of essentially absolute authority.
The Pope is the last "absolute" monarch on earth.
"It rides and falls on the contention that "Peter and his successors" have a connection that allows them to be the final say no matter what."
The whole concept of "Apostolic succession" is flawed. We do not have any "God Breathed" inspired writings in the Canon written after the Apostolic era. We have no supernatural powers passed on to any of the leaders that came after the Apostles. Peter being in Rome and the Bishop of that church wouldn't really change the argument against "Apostolic succession" if you read the Bible.