The following is taken from a book review of The Divine Primacy of the Bishop of Rome and Modern Eastern Orthodoxy. This review is by David E. Utsler. The words which follow are his but his thoughts so closely match my own I saw no need to try and put this into my own words:
There are five, universally recognized, ancient patriarchates in the Church. They are Rome, Constantinople, Jerusalem, Antioch, and Alexandria. These patriarchates and every subsequent one – every bishop and every diocese thereafter – were established in succession to the original twelve Apostles commissioned by Jesus. Just as the other eleven Apostles were not mere legates of Peter, neither are the other successors of the Apostles legates of the successor of St. Peter, the Pope. However, just as Peter was the head of the College of Apostles and was entrusted with preserving the unity of the apostolic college, so must the successors of the Apostles maintain visible communion with the successor of St. Peter.
St. Irenaeus of Lyons said of the Church of Rome:
"For with this church, by reason of its preeminence, the whole Church, that is the faithful everywhere, must necessarily be in accord" (Catechism, no. 834).
What is the nature of this visible communion? Eastern Orthodox theology has traditionally recognized a special dignity of the great patriarchate of Rome. The Bishop of Rome is considered to have a "primacy of honor" and to be a "chief among equals." The single greatest point of division between the Catholic Church and Eastern Orthodoxy is the nature of Peter's primacy. Is it a primacy of jurisdiction or one of mere honor?
As one who almost became Eastern Orthodox myself, I have often been puzzled by a few questions. If the primacy is one of honor, what is the reason for Rome having it? Did it derive from the geo-political position of Rome at the time? If so, Rome's primacy can't in any sense be permanent, as it is too connected to temporal affairs which are subject to change. If this is so, then it makes no sense for Eastern Orthodox theologians to continue to maintain that Rome has a primacy of honor. Is there a theological basis for a mere primacy of honor? If so, we can ask once more – why Rome? Why the See of Peter? What exactly is a primacy of honor? Does it mean getting to sit at the head of the table at official meetings? Though the power of genuine honor shouldn't be underestimated, what is the reason for acknowledging Peter's primacy of honor?
The real issue is the ongoing tension between Peter's primacy of jurisdiction and the collegiality of all the bishops. The "fatal error" of the Eastern Churches separated from Rome, Likoudis quite rightly points out, is to "consider Primacy and Collegiality... to be antithetical to one another" (xiv). The truth is that primacy without collegiality is a form of ecclesiastical totalitarianism and a collegiality without primacy is doomed to become a collegiality in name only. Is it possible to say that there exists a true collegiality among the Orthodox Churches today? There is a much more concrete collegiality between the current Bishop of Rome and many ecumenically minded Orthodox patriarchs than there is among many Orthodox bishops among themselves! (more here).