Father John Meyendorff was mentioned earlier. Here's his section on primacy. I don't see how it can be said to support the idea that the Pope of Rome is the exclusive successor of Peter, or has the primacy because he is the successor of Peter and not because he is bishop of the capital.
It is well worth reading. I have included the whole text including passages that might be seen to support the RC position as well as Father John's opposing arguments.
Father John writes:
"Most of the controversy which set Greek against Latin in the Middle Ages could have been solved easily if both churches had recognized a common authority able to solve the unavoidable differences created by divergent cultures and historical situations. Unfortunately, behind the various doctrinal, disciplinary, and liturgical disputes stood an ecclesiological dichotomy. Any historian today would recognize that the medieval papacy was the result of a long doctrinal and institutional development in which the Eastern Church had either no opportunity or no desire to participate. Orthodox and Roman Catholics still argue whether this development was legitimate from the point of view of Christian revelation.
The reformed papacy of the eleventh century used a long-standing Western tradition of exegesis when it applied systematically and legalistically the passages on the role of Peter (especially Mt 16:18, Lk 22:32, and Jn 21:15-17) to the bishop of Rome. This tradition was not shared by the East, yet it was not totally ignored by the Byzantines, some of whom used it occasionally, especially in documents addressed to Rome and intended to win the popes' sympathy. But it was never given an ultimate theological significance. The personal role of Peter as the "rock" upon which the Church was built was readily recognized by Byzantine ecclesiastical writers. Only late polemicists, systematically anti-Latin, tended to diminish it; but this was not the case among the most enlightened of the Byzantine theologians. Thus, according to Photius, Peter is "the chief of the apostolic choir, and has been established as the rock of the Church and is proclaimed by the Truth to be keybearer of the Kingdom of Heaven." 15 Numerous passages, similar to that of Photius, can be found in Byzantine ecclesiastical literature and hymnography. Their true significance, however, cannot be understood apart from more general presuppositions on the nature of the Christian faith and the manner of its preservation and continuity in the Church.
Origen, the common source of patristic exegetical tradition, commenting on Matthew 16:18, interprets the famous logion as Jesus' answer to Peter's confession: Simon became the "rock" on which the Church is founded because he expressed the true belief in the divinity of Christ. Origen continues: "If we also say 'Thou art the Christ, the Son of the living God,' then we also become Peter . . . for whoever assimilates to Christ, becomes rock. Does Christ give the keys of the kingdom to Peter alone, whereas other blessed people cannot receive them?" 16 According to Origen, therefore, Peter is no more than the first "believer," and the keys he received opened the gates of heaven to him alone: if others want to follow, they can "imitate" Peter and receive the same keys. Thus the words of Christ have a soteriological, but not an institutional, significance. They only affirm that the Christian faith is the faith expressed by Peter on the road to Caesarea Philippi. In the whole body of patristic exegesis, this is the prevailing understanding of the "Petrine" logia, and it remains valid in Byzantine literature. In the twelfth-century Italo-Greek homilies attributed to Theophanes Kerameus, one can still read: "The Lord gives the keys to Peter and to all those who resemble him, so that the gates of the Kingdom of heaven remain closed for the heretics, yet are easily accessible to the faithful." 17 Thus, when he spoke to Peter, Jesus was underlining the meaning of the faith as the foundation of the Church, rather than organizing the Church as guardian of the faith. The whole ecclesiological debate between East and West is thus reducible to the issue of whether the faith depends on Peter, or Peter on the faith. The issue becomes clear when one compares the two concepts of the succession of Peter.
If many Byzantine ecclesiastical writers follow Origen in recognizing this succession in each believer, others have a less individualistic view of Christianity; they understand that the faith can be fully realized only in the sacramental community, where the bishop fulfills, in a very particular way, Christ's ministry of teaching and, thus, preserves the faith. In this sense, there is a definite relationship between Peter, called by Christ to "strengthen his brethren" (Lk 22:32), and the bishop, as guardian of the faith in his local church, The early Christian concept, best expressed in the third century by Cyprian of Carthage, 18 according to which the "see of Peter" belongs, in each local church, to the bishop, remains the longstanding and obvious pattern for the Byzantines. Gregory of Nyssa, for example, can write that Jesus "through Peter gave to the bishops the keys of heavenly honors." 19 Pseudo-Dionysius, when he mentions the "hierarchs"-i.e., the bishops of the earthly Church-refers immediately to the image of Peter. 20 Examples taken from the later period, and quite independent of anti-Latin polemics, can easily be multiplied. Peter's succession is seen wherever the right faith is preserved, and, as such, it cannot be localized geographically or monopolized by a single church or individual. It is only natural, therefore, that the Byzantine will fail to understand the developed medieval concept of Roman primacy. Thus, in the thirteenth century, shortly after the capture of Constantinople by the Crusaders ( 1204), we can read Nicholas Mesarites, addressing the Latins:
You try to present Peter as the teacher of Rome alone. While the divine Fathers spoke of the promise made to him by the Savior as having a catholic meaning and as referring to all those who believed and believe, you force yourself into a narrow and false interpretation, ascribing it to Rome alone. If this were true, it would be impossible for every church of the faithful, and not only that of Rome, to possess the Savior properly, and for each church to be founded on the rock, i.e., on the doctrine of Peter, in conformity with the promise. 21
Obviously, this text of Mesarites' implies a concept of the Church which recognizes the fullness of catholicity in each local church, in the sense in which the Apostolic Fathers could speak, for example, of the "catholic church sojourning in Corinth." Catholicity, and therefore also truth and apostolicity, thus become God-given attributes belonging to each sacramental, Eucharist-centered community possessing a true episcopate, a true Eucharist, and, therefore, an authentic presence of Christ. The idea that one particular church would have, in a full theological sense, more capacity than another to preserve the faith of Peter was foreign to the Byzantines. Consensus of bishops, and not the authority of one particular bishop, was for them the highest possible sign of truth. Hence their constant insistence on the authority of the councils and their inability to understand the Roman concept of the papacy. It is not, however, that the very idea of primacy was foreign to the Byzantines; but they generally understood it as a matter for conciliar legislation, not as a God-given function of a particular church.
One important difference between eastern and western attitudes deserves particular emphasis. . . . The idea of apostolicity played a very limited role in the development of the Church in the eastern provinces, but . . . Rome owed its prestige in Italy and in other western provinces . . . to the veneration in which young Christian communities of the West held St. Peter . . . whose successors the Roman bishops claimed to be. 22
Historians have often cited the fact that Rome was the only local church of the West which could claim "apostolic" foundation and attract pilgrimages ad limina apostolorum. In the East, innumerable cities, or lesser localities, could authentically attribute their foundation to Peter, Paul, John, Andrew, or other Apostles. These various "apostolicities" did not entail any jurisdictional claims: the bishop of Jerusalem was still, in the fourth century, only a suffragan of the metropolitan of Caesarea, the civil capital of Palestine.
When the Council of Nicaea, in its famous Canon 6, vaguely mentioned the "ancient customs" which recognized an exceptional prestige to the churches of Alexandria, Antioch, and Rome, the selection of these particular churches was determined not by their apostolic foundation, but by the fact that they were located in the most important cities of the empire.
For if apostolicity were the criterion, as later Western interpretations insist, the position of Alexandria, purported to have been founded by a minor apostolic figure, Mark, could not be greater than Antioch's, where Peter's presence is attested by the New Testament.
The East remained pragmatic in its definition of universal or local primacies among the churches, and this attitude made conflict inevitable as soon as Rome recognized an absolute and dogmatic significance to the "apostolic" criterion of primacy. Actually, in the Byzantine Empire, "pragmatism" meant adjustment to the structure of the state, and this adjustment explains the text of Canon 28 of the Council of Chalcedon:
The Fathers rightly granted privileges to the throne of old Rome, because it was the imperial city. And one hundred and fifty most religious bishops [of Constantinople, 381], actuated by the same considerations, gave equal privileges to the most holy throne of new Rome, justly judging that the city, which is honored with the presence of the emperor and the senate and enjoys equal privileges with the old imperial Rome, should, in ecclesiastical matters also, be magnified as she is and rank next after her.
This text was in no way meant to suppress the prestige of Rome (it was directed against the pretentions of Dioscorus of Alexandria, whom the Council of Chalcedon deposed); but it certainly excluded the "Petrine" interpretation of Roman primacy, and
was in conformity with the logical development of ecclesiastical organisms in the Byzantine period which, since the era of Constantine, had admitted the principle that ecclesiastical administration coincided with the secular structure of the Empire. 23
As we have seen above, the succession of Peter was considered to be involved in the episcopal office present in every church, and was envisaged as a responsibility in which any "successor of Peter," including the bishop of Rome, could fail. A theologian of the fifteenth century, Symeon of Thessalonica, could thus write:
One should not contradict the Latins when they say that the bishop of Rome is the first. This primacy is not harmful to the Church. Let them only prove his faithfulness to the faith of Peter and to that of the succes. sors of Peter. If it is so. let him enjoy all the privileges of Peter. . . . "