The See That Judges All Is Judged by None

Every claim made for the papacy is held to follow from one fact, that the pope is the Bishop of Rome, and the most consequential feature of the office is that nothing stands above it.

What Vatican I defined

Catholic teaching holds that Peter received a primacy from Christ and that the Bishop of Rome inherits it. The First Vatican Council in 1870 defined what this authorises: universal, immediate and ordinary jurisdiction over the whole church, so that the pope can act directly in any diocese without going through its bishop, and infallibility when he defines a doctrine of faith or morals to be held by the whole church. That last power is narrow and has been used sparingly; the usual reckoning is that it has been exercised unambiguously once since it was defined, for the Assumption in 1950.

No mechanism of removal

A pope holds office until death or resignation. Resignation is provided for in canon law and is rare, Benedict XVI in 2013 being the first to resign freely since Celestine V in 1294. There is no mechanism for removing a pope, which is a structural fact of consequence: the see that judges all is judged by none. The Orthodox churches accept the Bishop of Rome as first in honour among patriarchs and reject the jurisdictional and infallible claims, and that rejection is the substance of the schism rather than an ornament on it.