The Greeks were consistently interpreting the 3 passages (Matt 16, John 21, Luke 23) as pertaining to Peter’s primacy, and via inheritance, the prerogative of Peter’s chair. Below is a florigelium of Greek interpretation from the 5th to 9th centuries:
St. +Cyril of Alexandria, writing in his commentary on the gospel according to St. Matthew (444), says, “that by the words ‘on this rock I shall build my church’, Christ makes Peter its Pastor, literally he places Peter over it as shepherd” – Ταύτης ποιμένα τόν Πέτρον έφίστησω (Patrologia Graeca 72, 423)
St. + Gregory of Nyssa, spoke in a recorded sermon (395) saying that Peter is the head of the Church, “According to the privilege granted him by the Lord, Peter is that unbreakable and most solid rock upon which the Savior built His church” – ή άρραγής καί όχυρωτάτη πέτρα έφ ήν τήν Έκκλησίαν ό Σωτήρ ώκοδόμησε (Patrologia Graeca 46, 733)
St. John Chrysostom taught that St. Peter was the “leader of the Apostles” in his 88th homily in St. John’s gospel (PG 59, 478), and even went further than this. In his 5th homily on “Penitence”, Chrysostom writes that after Peter had been restored to his former apostleship after committing the three-fold denial, he was also given “jurisdiction over the universal church” (PG 49, 308).
Again, in his 8th discourse on the Jews, he writes on how the repentance of Peter wiped out his fault and , “he becomes again head of the Apostles and the whole world is committed to his care” (PG 48, 951)
During the Monophysite fall out in the East, there were bishops who were strongly Chalcedonian, and thus, wished above all to retain the communion of the Apostolic See. A famous letter of appeal was written to Rome, and these Greeks openly declared the following about Pope Symmachus (512 AD):
“…but for the precious salvation not only of the East, but of three parts almost of the inhabited world, redeemed, not with corruptible gold or silver, but with the precious blood of the Lamb of God, according to the doctrine of the blessed prince of the glorious Apostles, whose See Christ, the Good Shepherd, has entrusted to your blessedness….You have not only received the power of binding, but also that of loosing, in accordance with the example of the Master, those who long have been in bonds, nor only the power of uprooting and of destroying, but also that of planting and rebuilding, as Jeremias, or rather, as Jesus Christ, of whom Jeremias was the type….You are not ignorant of this malice, you whom Peter, your blessed Doctor, teaches always to shepherd, not by violence but by an authority fully accepted, the sheep of Christ which are entrusted to you in all the habitable world.” (Mansi viii. 221)
“Two bishop of Thessalonica wrote the following to Pope Boniface II (521): “For these things we appeal to your blessedness and the Apostolic See, and through it we believe we hear and adore thrice blessed Peter, and the chief Shepherd of the Church, Christ our Lord” (Mansi, viii, 748)
Patriarch St. Sophronius of Jerusalem had commissioned St. Stephen of Dor to appeal to the Roman See in order to procure the condemnation of the Monothelites occupying the Eastern Patriarchates. Stephen describes this aloud at the Council of Lateran 649:
““And for this cause, sometimes we asked for water to our head and to our eyes a fountain of tears, sometimes the wings of a dove, according to holy David, that we might fly away and announce these things to the Chair which rules and presides over all, I mean to yours, the Head and Highest, for the healing of the whole wound. For this it has been accustomed to do from of old and from the beginning with power by its canonical and apostolical authority, because the truly great Peter , head of the Apostles, was clearly thought worthy not only to be entrusted with the keys of heaven, alone apart from the rest, to open it worthily to believers, or to close it justly to those who disbelieve the gospel of grace, but because he was also first commissioned to feed the sheep of the whole Catholic Church; for ‘Peter’, said He, ‘Do you love me? Feed my sheep’, and again , because he had in a manner peculiar and special, a faith in the Lord stronger than all and unchangeable, to be converted and to confirm his fellows and spiritual brethren when tossed about, as having been adorned by God himself, incarnate for us, with power and sacerdotal authority…I was urged by the requests of almost all the pious bishops of the East in agreement with the departed Sophronius…Without delay I made this journey for this purpose alone; and since then thrice have I run to you Apostolic Feet, urging and beseeching the prayer of Sophronius and of all, that is, that you will assist the imperiled faith of Christians”” (Acts of Lateran Synod 649, Richard Price)
St. Theodore the Studite (+826) wrote a letter to Pope Paschal I, and in it reads:
“Hear me, O Head of the Apostles, placed by God as Shepherd of the Sheep of Christ, holder of the keys of the kingdom of heaven, the rock of faith on which the Catholic Church has been built. For you are Peter; you adorn the throne of Peter and rule from it” (PG 99-1151).
And as insincere as one would like to think it is, the words of Photius the Great (9th century) to Pope John VIII:
“We may well ask who is the Master who has taught you to act in this fashion? — surely, above all, it is Peter, the leader of the Apostles whom the Lord has placed at the head of all the churches, when He said to him: ‘Feed my sheep’. ” (Mansi 17, 396D; MGH, Epp. VII, 167)