+Ioannis of Pergamon is the co-chairman of the committee on the Ctahoic-Orthodox Dialogue and his one of the few Orthodox bishops who see papacy in the light of Matthew 16. St. John Chrysostom was likewise one of few (+Maximos the Confessor comes to mind), who sought refuse in Rome during an Eastern heresy, who was a biblical "papist."
But the Church as a whole wasn't. Sure, papal legates at the Council of Chalcedon referred to the successor of Peter as the the "ruler of the Church," but the bishops, by their vote on Canon XXVIII demonstarted a different opinion of the Bishop of Rome.
They actually made sure to qualify, as they have in a Council preceding it, lest tere be no misunderstanding, that the privilege and honor of the Bishop of (elder) Rome was entirely due to the imperial dignity of the elder Rome, and that these privileges were given to the pope by the very same bishops!
Read the proceedings of the Council and see it for yourself. In other words, the Church, not one Eastern bishop (i.e. St. John Chrysostom) in the 5th century did not buy into the Latin interpretation of Matthew 16:19 or any biblical authority of the pope. And they made that known for all posterity.
Today, as in the past, the majority of Eastern bishops do not see papacy in the light of Matthew 16:19 and point to the fact that the verse is in the future tense ("I will give you") and that in Matthew 18:18 the same is given to all the disciples.
We can literally talk until kingdom come, and neither side will have a clear-cut argument for their position. The Cathjoic-Orthodox Dilaogue on the nature of the primacy of +Peter has been going on for years now, and they have not been able to come up with a joint statement as they have on the filioque (which didn;t give any positive fruit whatsoever because it is being ignored!).
This is why I keep saying it is best if we fraternally embrace each other on those issues we share in common and leave our dogmatic differences in peace without judgment. Pressing for re-union creates artificial hope in people who are not familiar with what keeps us apart, and that's rather deceptive in my opinion.
Again, I do not try to argue anything the Fathers of the Church did not teach. I am, after all, Catholic. The authors of the Encyclical, however, mislead their flock as regards to the patristic teaching on the confession of Peter, the nature of the grant of the keys, and the charge to Peter. I showed why.