Dear Jack,
If we go back to the OP, and to some of the earlier posts, we see that the ECFs took the view that Rome had a primacy of honour; it is the definition of what that means which has contributed to the problems in the Church.
If we look at another of the pillars of Holy Tradition, the Councils, we can see from the canons of Nicaea that Rome was not, at that time, claiming jurisdictional authority over, for example, Alexandria (look at canon 6). That said, Alexandria certainly consulted Rome, as did the other Patriarchal Sees, so to argue that in the early Church Rome was not primus inter pares would be wrong.
What we see before the fifth century is a tradition of honour to Rome which, before then, needed no close definition as no one claimed anything attached to it by way of jurisdiction. However, with the collapse of the Western Empire, it became very important in the West that Rome, as the sole Apostolic See, was recognised as having jurisdictional authority. At no point before the sixteenth century did people in the West challenge that; those in the West who departed from that custom and practice have their reasons for so doing; nonetheless, they did depart from ancient custom.
In the East, where there was no collapse of the Empire, and where Rome had not had jurisdictional authority, the claims of Leo I were heard, but not concurred with. It was only with the Arab invasions and the disappearance from the scene of Alexandria, Antioch and Jerusalem, that the trouble between Constantinople and Rome began to become severe. The other Sees had always played a collegial role; without them there were two centres, using two different languages and with two different secular powers; it is hardly surprising that trouble came.
So, to sum up. The East is right to claim it never understood the Petrine verses as giving the Bishop of Rome more than a primacy of honour; but then it has never defined what that means. The West is also right in claiming that its understanding of the Petrine claims developed as they have; but its definition is not, I suspect, as well understood as it ought to be; the looseness with which non-Catholics write about Infallibility often suggest a reaction to a particular notion of what it means rather than an accurate appreciation of its reality.
This explains why all sides in this dispute can stake a claim for their own tradition; we are, in fact, dealing with different traditions which interpret an originally broad and vague understanding (what, after all, does primacy of honour actually mean?) with more precision than it was given in times when everyone thought they knew what it meant.
peace,
Anglian