If the primacy of Peter – whatever that primacy is – is in fact of divine origin, coming from the will of Christ, and if the primacy of Rome is directly related to this primacy of Peter, then the question arises: Who is more likely to have the correct understanding of that primacy – the church that has office of Peter or the church that does not?
If one does not claim a divine origin for Peter’s primacy or Rome’s primacy, but says that the primacy relates more to Rome’s place in the empire, for example, then the issue is a bit different.
I’m not really sure how the Orthodox view the divine basis for Peter’s primacy. But if they do think it is of Christ’s will, then the dilemma above follows, I think.
Orthodox Christians believe that the primacy St. Peter held is akin not to one bishop above other bishop, but to one bishop over his flock. In other words, the successor of Peter is the bishop in each church, not only the Bishop of Rome. One finds evidence of this in church history:
“Our Lord, whose precepts and warnings we ought to observe, determining the honour of a Bishop and to the ordering of His own Church, speaks in the Gospel, and says to Peter, I say unto thee, That thou art Peter, and on this rock will I build My Church; and the gates of hell shall not prevail against it. And I will give unto thee the keys of the kingdom of heaven: and whatsoever thou shalt bind on earth shall be bound in heaven; and whatsoever thou shalt loose on earth shall be loosed in heaven (Matt. 16:18-19). Thence the ordination of Bishops, and the ordering of the Church, runs down along the course of time and line of succession, so that the Church is settled upon her Bishops; and every act of the Church is regulated by these same Prelates.” St. Cyprian, 33rd Epistle.
St. Cyprian directly ties the promise of Christ to St. Peter to the office of the episcopacy as a whole, not just to Rome.
“66. Priests Britain has, but foolish ones; a great number of ministers, but shameless; clergy, but crafty plunderers; pastors, so to say, but wolves ready for the slaughter of souls, certainly not providing what is of benefit for the people, but seeking the filling of their own belly. They have church edifices, but enter them for the sake of filthy lucre; they teach the people, but by furnishing the worst examples, teach vice and evil morals; they seldom sacrifice, and never stand among the altars with pure heart; they |165 do not reprove the people on account of their sins, nay, in fact, they commit the same; they despise the commandments of Christ, and are careful to satisfy their own lusts with all their prayers:
they get possession of the seat of the apostle Peter 61 with unclean feet, but, by the desert of cupidity,62 fall into the unwholesome chair of the traitor Judas.”
-St Gildas, De Excidio Britanniae: St. Gildas identifies bishops, and multiple bishops at that, as successors of Peter and possessers of his chair.
“I beseech our common father Ambrose, that, after the scanty dew of my discourse, he may pour abundantly into your hearts the mysteries of the divine writings. Let him speak from that Holy Spirit with which he is filled, and ‘from his belly shall flow rivers of living water;’ and,
as a successor of Peter, he shall be the mouth of all the surrounding priests. For when the Lord Jesus asked of the apostles, ‘Whom do you say that I am?’ Peter alone replies, with the mouth of all believers, ‘Thou art the Christ, the Son of the living God.’ What reward did that confession at once receive? Blessedness indeed, and the most glorious power of the heavenly kingdom.”
-St. Gaudentius of Brescia (Tract. 16, De Ordin. Ipsius. Cited by J. Waterworth S.J., A Commentary (London: Thomas Richardson, 1871), pp. 105-107).