While I must admit, I am flattered to be described as "an Orthodox priest with Origen at his fingertips," I'm afraid I must disavow the compliment. (Hmm... Come to think of it, he did say "Origen at his fingertips..." Perhaps it wasn't meant as a compliment! :-) ) I merely spent a few hours last night using Google and the Christian Classics Ethereal Library - it was actually astonishingly easy to find patristic exegesis that corresponded with what I was at first inclined to concede was a relatively recent Protestant innovation. I guess if you hear something often enough, you are inclined to believe it is true!
In fact, without intending any disrespect to Gabriel - who did, after all, say a bunch of nice things about us in his original post! - I am continually astonished at the logical gaps in the traditional Catholic defence of the papacy. Orthodox Christians have never (or a least rarely!) denied that the bishop of Rome was worthy of a primacy of honour - although the basis for this primacy was not understood to be merely Rome's antiquity or her connection to Sts. Peter and Paul, both of which Rome shares (as has been noted) with the patriarchate of Antioch, but also a function of the conservatism (i.e., fidelity to the apostolic teaching) and influence of the Roman church. It was by virtue of the combination of these factors that Rome was also commonly referred to as an arbiter in difficult canonical disputes.
That being said, it is a long logical leap from a primacy of honour - or even from the role of referee - to the relatively recent claims of absolute supremacy and infallibility made by the modern Roman papacy. It is certainly true that the Apostle Peter took the leading role in the early Church, but this was by no means an absolutely authoritative or infallible role, as can be seen in the part Peter played in precipitating the Jew-Gentile controversy in Antioch and in the leading role that St. James played in pronouncing the collegial judgement of the council of Jerusalem. Nor is there any evidence that the early Church understood the role of the bishops of Rome or their connection to Peter (indeed, most early references are to the connection with Sts. Peter and Paul) as granting them anything like the authority and infallibility that is claimed by the modern papacy. This is the point of the long (probably over-long!) patristic quotes I cited below from Augustine and Origen - unlike as they were, and authoritative as Augustine is (in the West, at least), both explicitly make the point in their exegesis of Matthew 16:18 that our Lord was not saying that Peter himself is the source of the unity and infallibility of the Church.
It is all well and good to talk about needing to "breathe with both lungs, East & West" - and in fact we do appreciate the many overtures and gestures of good faith made by Pope John Paul II and his successor, Pope Benedict XVI; no one wants to return to the bad old days of high-tension East-West relations! - but to portray the Petrine office as the ultimate source of unity in the Church is ultimately non-Scriptural, not Patristic, and untrue! I hope and pray one day for a real reunion with Rome - a reunion of equals in which the Roman primacy of honour is something given freely and willingly, based on the fidelity of the Roman Church to the teachings and the practice of the apostles. In short, our only hope for ultimate unity lies in our mutual submission and fidelity to one another, to the apostolic tradition, and, above all, to Him who is alone our supreme and infallible Head, our Lord Jesus Christ, the Way, the Life, and the Truth!