[FormerLib]

No, they argued about "which of them should seem to be the greater". That's not necessarily a reference to authority.

I'm sorry, but how does greater authority not make make one "greater" in regards to authority on this earth.

Your statement contradicts itself.

[gbcdoj]

I'm sorry, but how does greater authority not make make one "greater" in regards to authority on this earth.

One could be greater in other ways than authority.

Really, all the Fathers agree, as you know, that some kind of primacy was conferred upon St. Peter by St. Matthew 16:18-19. I can't believe that it's necessary to prove this to you Orthodox who should respect their authority.