OK:
Let me break it down for you.
1. Antioch, by ROMAN belief should have primacy, as St. Peter was Bishop THERE first. (NOT ORTHODOX)
2. Primus inter pares was given to the Bishop of the IMPERIAL CITY. Rome was the Imperial Capitol of the empire, so that title had nothing to do with Rome’s claim of primacy by virtue of Peter. Later, the title was given to the Ecumenical Patriarch of Constantinople.
Last, but not least, my point in all this is that the doctrine of Peterine Primacy is an invention of the Western, or Latin Church, mainly based on the spurious writings of Clement, and that other than being the “First among EQUALS”, there was no universal authority conferred on Rome.
Clement’s First Epistle to the Corinthians is genuine, written in the 90’s AD. The second one, attributed to him, there is good evidence to believe was not his own. But even that evidence points to a date of about AD 150. It is still useful for the purpose of this discussion, though, since, with such a still relatively early provenience, it is a witness to the already accepted tradition of only 50 years earlier.
But, even apart from Clement, there is a lot of early evidence that Peter’s protracted ministry in Rome and his martyrdom there were universally understood and accepted. Is St. Irenaeus merely a Roman stooge in Against Heresies 3? Is Tertullian merely ignorant when he talks about Clement’s ordination by Peter in Rome? Does Cyprian know what he’s talking about when he states baldy that it was upon Peter that Christ built His Church? Does Pope Victor know what a troglodyte he was when he threw his weight around the universal Church, as Bishop of Rome, during the Quartodeciman controversy?
Look, the primacy of Peter is Christ-established and disciple-confirmed. It is an ecclesiastical exercise in revisionist history to claim that no one in the early Church had any notions of papal primacy until Gregory the Great came along. Sure, that primacy has been used in a heavy-handed manner form time to time, but the principle of its existence is pefectly valid. Thank God that the Church had a visible head amid all of the heresies promulgated, primarily in the East, in the patristic age!
It seems to me that you must belong to a brand of eastern Orthodoxy that likes the trappings of a liturgical Church, but is so hell-bent on denying the legitimacy of Rome’s claims that it must deny much of the early writings and traditions at the same time. Orthodoxy, like Catholicism, finds much of its roots in the early patristic writings. Don’t ignore the legitimacy of many of the early Fathers just to score spurious talking points against Rome.