from Catholic Answers:
THE EPIPHANY OF THE ROMAN PRIMACYcatholic.com/thisrock/1997/9702eaw.asp
…Eastern Orthodox apologists’ case against Petrine primacy is based almost entirely on their reading of early Church history. For many of the leading Orthodox theologians of this century, that reading is controlled by the theory which they call “Eucharistic ecclesiology” or “local-church ecclesiology.” (In Orthodox usage, as in Catholic usage, “local church” designates a diocese, not a local congregation.)
Some Orthodox ecclesiologists repeatedly invoke one sentence from the letter of Ignatius to the Smyrnaeans: “Where the bishop appears, there let the people be, just as where Jesus Christ is, there is the Catholic Church.” This, they say, means that the fullness of the Church is found in each local church. No local church can exercise authority over any other local church.
This Orthodox axiom consistently was contradicted by events in early Church history. About A.D. 96, for example, in the pontificate of Clement I, a faction in the Church in Corinth created a schism by ousting some bishops and presbyters. Clement wrote a strongly worded letter to that Church. He begins his letter apologizing for his delay “in giving our attention to the subjects of dispute in your community.” Vigorous persecution of the Church, especially at Rome, under Nero and Domitian, had prevented the Church of Rome from intervening earlier.
Clement immediately addresses the perpetrators of the schism, calling their action “that execrable and godless schism so utterly foreign to the elect of God.” He reproves them for presuming to assert authority over successors of the apostles. Their action, he says, is “no small sin.” He does not ask for more details in order to make his judgment. He simply passes judgment on the schismatics and orders them to submit to their pastors.
In what one author has called “the epiphany of the Roman primacy,” Clement commands the schismatics to be “obedient to what we have written through the Holy Spirit.” He warns them, “But should any disobey what has been said by him [Christ] through us, let them understand that they will entangle themselves in transgression and no small danger.”
Clement hardly could assert more strongly his assurance that the Holy Spirit is speaking through him and therefore that he, Clement, speaks with the voice of Christ. He concludes by saying he has sent three legates to Corinth to investigate the situation. From other sources we know the schism was healed by Clement’s action.
Had the Church at Corinth appealed to Clement to settle the schism? That Clement apologizes for delay in intervening suggests it had. The Corinthians were not simply seeking help from some authoritative person. Were that true, they could have appealed to the apostle John. According to early testimony, at that time he was still living and in a city (Ephesus) much closer to Corinth than was Rome. No, they appealed to the successor of Peter. At the end of the first century, Rome’s authority and responsibility for settling such matters was already recognized.
No local church could exercise authority over another local church? The Corinthians never heard of this notion. How did they respond to Clement’s intervention? They held Clement’s letter in almost as high esteem as they did sacred Scripture. Eusebius tells us that seventy years after Clement sent his letter, the Church at Corinth was still reading aloud from it every Sunday during the liturgy.
Petrine authority was not, as Easterners claim, a papal invention to impose a theological straitjacket on the unsuspecting East. No, that authority was always a lifeline to the truth. Again and again by that lifeline Easterners were rescued from the Frankensteinian heresies they so readily created but could not overcome.