Summary: Over two millenia there have, of course, been many papal claims, many of which Orthodoxy has always accepted. The claim to be the Patriarch of the West has proved unobjectionable to the East. The claim to be the primate of the Church is also unobjectionable, though this one requires some historical context. It is the claims explicated in detail at the First Vatican Council of 1870 that have proved the sticking point. But let us proceed slowly and carefully.
