Of course eastern Christians are going to argue against it.
But here is one better, eastern FATHERS arguing FOR it:
Eastern Fathers and the Primacy of Peter
The quotes are very powerful.
It seems to be that Jesus gave the keys of the kingdom to Peter. He called him "rock" for a reason. He held a special place and his special role was described in John 21.
There has to be someone, something on which the Church can visibly be centered on Earth. There has to be a rock where we can find the Church.
"If the Roman See recognizes Pyrrhus to be not only a reprobate but a heretic, it is certainly plain that everyone who anathematizes those who have rejected Pyrrhus also anathematizes the See of Rome, that is, he anathematizes the Catholic Church. I need hardly add that he excommunicates himself also, if indeed he is in communion with the Roman See and the Catholic Church of God ...Let him hasten before all things to satisfy the Roman See, for if it is satisfied, all will agree in calling him pious and orthodox. For he only speaks in vain who thinks he ought to pursuade or entrap persons like myself, and does not satisfy and implore the blessed Pope of the most holy Catholic Church of the Romans, that is, the Apostolic See, which is from the incarnate of the Son of God Himself, and also all the holy synods, accodring to the holy canons and definitions has received universal and surpreme dominion, authority, and power of binding and loosing over all the holy churches of God throughout the whole world."
-- Saint Maximus the Confessor, whom would be considered a blatant heretic in the east today if he said such things