Some fathers teach this. Many more fathers teach that the Church is built on Peter's confession of faith.
Perhaps you can enlighten us as to what terrible heresy has been tearing at the unity of the Church since the schism. None of the Ecumenical Councils were held on a whim, but only in response to serious falsehood spreading within the Church. The so called ecumenical councils which have been held in the West since that time, many of them anyway, are the complete antithesis of those held before the schism. There is also the fact that the term "ecumenical" was tied in with the Roman empire and particularly its capital, which had been moved to Constantinople. That empire has ceased to exist for centuries now, so it would be strange to call a new council by the title of "ecumenical".
We have had several pan-orthodox councils since that time, but nothing in response to anything so serious as experienced by the Church in the first few centuries.
Of course I agree that the Church is built on Simon Rock's confession of faith. That would also support the Papal claims.
But as I far as I can tell, it's not just "some fathers" who say the Church is built on Simon Rock. It is the plain meaning of Scripture AND the teaching of the very fathers who say the Church is ALSO built on Peter's Confession.
There are many fathers who say the Church IS built on Peter. I know of some of them: HippolytusHilary, Basil, Chrysostom, the Council of Chalcedon, Epiphanius, Ephrem, Leo, Gregory Nazianzen, Gregory of Nysaa.
Dave Armstrong says that the following fathers held it was Peter, not his faith or confession, that is the rock on which the Church is built:
Tertullian
Hippolytus
Origen
Cyprian
Firmilian
Aphraates the Persian
Ephraim the Syrian
Hilary of Poitiers
Zeno of Africa
Gregory of Nazianzen
Gregory of Nyssa
Basil the Great
Didymus the Blind
Epiphanius
Ambrose
John Chrysostom
Jerome
Augustine
Cyril of Alexandria
Peter Chrysologus
Proclus of Constantinople
Secundinus (disciple and assistant of St. Patrick)
Theodoret
Council of Chalcedon
How many fathers said the Church is NOT built on Peter, or that it is built ONLY on his confession?
Also, Pope St. Leo is regarded by the Orthodox as a saint. But didn't he claim Papal Supremacy?
Also, my sources say that the Council of Chalcedon said that Leo was stripping Dioscorus of his episcopate THROUGH THEM. Do you know about that. Why would they say that it was Leo who was doing the disciplining through them. Why not just strip him of his bishopric themselves?
As to the rest I'll have to think about it. I don't know history well. But I know that the "Reformation" was quite a great heretical crisis.