The reason I bring up this question (and to provide a little background on myself) is I was raised Roman Catholic and am close to completing my conversion to the Orthodox faith. What I recall being taught as a child was there was an unbroken line of succession back to the first pope, Peter. Now, perhaps I was taught about the 5 jurisdictions in the early years of the church (Rome, Constantinople, Antioch, Alexandria, Jerusalem) but I honestly can not remember this. Maybe I fell asleep during class that day.

So right now as an adult I operate under the impression I was not taught of these 5
equal jurisdictions in the early years.
Orthodox readings thus far, such as Timothy Ware's book, emphasize the equality between the 5 as has my priest in his instruction. The book refers to Peter as the first bishop of Rome, as the other cities also had bishops. The Patriarchates today trace their lines back to their respective first bishops and so forth. I suppose what I'm asking is what was it during the later years but pre-1054 that led Rome on a path to attempt to claim supremacy over all others on which the Catholic church still holds to today.
"What I recall being taught as a child was there was an unbroken line of succession back to the first pope, Peter. "
Let's break that into two subjects:
- Unbroken succession;
- Peter, first pope;
Unbroken succesion is true, as it is that the Patriarch of Antioch *also* can trace an unbroken succesion to Peter, since this see was founded by the Apostle before Rome. It was the hand of Providence that Peter would have two direct lines of unbroken succession since if 1) Peter had been conceded supremacy and infallibility; 2) if these gifts were transmitted to his successors; 3) than necessarily both the Patriarch of Rome and of Antioch would have it. 3.1) In fact, considering that the Patriarch of Alexandria traces his own succession to Mark, the Evangelist, and Mark was a direct disciple of Peter (so much that some, like myself, believe that to be the Petrine Gospel), than maybe even the Patriarch of Alexandria *who held the title of Pope before the Roman bishop* would be fair game for infallibility and supremacy.
Indeed, if (1) Peter and his successors have supremacy over the church and also infallibility and since (2) we have two petrine successors and the Romans just one, I'd say that (3) either infallibility is true and therefore the Orthodox Church is the true One, Holy, Catholic and Apostolic Church, since two of three authorities agree and only one diverge; or infallibility is wrong and Rome's central claim is false.
Tertium non datur.
Now, for the Peter being the first Pope. Peter was most classically depicted as the corypheus of the Apostle. This is an important title because the Fathers who used it knew and certainly studied Greek theater very well. Here's how Wikipedia explains it:
Coryphaeus, or Koryphaios (Greek κορυφαῖος koryphaîos, from κορυφή koryphḗ́, the top of the head), and often corypheus in English. In Attic drama, the coryphaeus was the leader of the chorus. Hence the term (sometimes in an Anglicized form "coryphe") is used for the chief or leader of any company or movement. The coryphaeus spoke for all the rest, whenever the chorus took part in the action, in quality of a person of the drama, during the course of the acts.
Also, David Wiles in "Greek Theatre Performance" (
http://is.gd/sUtN4I ) writes:
"The coriphaeus waw both leader and teacher, and in performance played a crucial role in setting the time that the other dancers followed. However there is no evidence to support the common idea that the coryphaeus alone spoke the short passages of dialogue which are allocated to the chorus but not designated for dancing."
The parts in bold go to the crux of the issue.
The coryphaeus was leader and teacher. That is what Romans get for the "supremacy" idea. But the second part of each paragraph is equally important: the coryphaeus is such only as long as "he speaks for all the rest" (like Peter does in Mat. 16:18) and "during the course of the acts", "in performance", i.e., while *following the script*, in our case, while reciting the Orthodox Faith - which is precisely what happens in Mat 16:18:
One sees clearly that Jesus gives the keys to Peter *because* he had confessed the orthodox faith. If Roman ecclesiology were correct, than Jesus would have given the keys to Peter, and *because of them* he would have uttered the orthodox faith. In sum: authority is a consequence of defending the orthodox faith, like the Orthodox Church has been doing. It is not faith that is a consequence of authority.
In short:
Orthodox teaching: Divinely given orthodox faith provides ecclesiological authority.
Roman teaching: Divinely given ecclesiological authority provides orthodox faith.
I believe that Mat 16:18 stands firmly on the ground of the Orthodox teaching.
Also, the coriphaeus did not speak of himself. Ever. He, like the chorus, had to attain to the script of the play and the imagination of the playwriter. He was not even the director of the play. The playwriter was. So it was the playwritter who would "depose" and "instate" actors. It was the plawriter who would organize and guarantee the success of the play because he himself had written it and he knew what he wanted to convey.
That is exactly the role of the Holy Spirit in the Church. He is the playwriter and the director. He knows what He wants to convey. The bishop of Rome overstepped his role as coryphaeus and thought of himself as the "visible director" of the "invisible playwriter". People stopped trusting the True Director. That is why the second chanter, the Patriarch of Constantinople, was elevated to the role of Coryphaeus of the Church and the old coryphaeus built his own chorus to sing the songs they wrote themselves. Soon enough some of the singers thought they should create their own bands and Protestantism rose. Finally celebrity fever stroke some and they thought it would be great to have a "solo" career and that's how we came to this situation of hundreds of thousands of denominations and non-denominational churches. Each one singing their own songs, wanting to be more creative than the other and none in tune with the original play, except the ones that humbly kept the traditional order: the Orthodox Church.
So Peter was the first coryphaeus for sure. He spoke for the Apostles, and he spoke what he was told to by the Spirit in symphony with what all the others were saying. *Right after that* he dissonated and was reproached. His authority was completely dependent on the orthodoxy of his faith. It never guaranteed that he would always be orthodox or teach orthodoxily. In that sense, he was not the first "pope" because what the popes believe to be since Vatican I is clearly not what Peter knew he was. Peter has at least two direct succession lines and possibly a third. So, there is no possible angle where Roman doctrine holds water.