The Lord says to Peter: “I say to you,” he says, “that you are Peter, and upon this rock I will build my Church” . . . On him he builds the Church, and to him he gives the command to feed the sheep John 21:17], and although he assigns a like power to all the apostles, yet he founded a single chair [cathedra], and he established by his own authority a source and an intrinsic reason for that unity. Indeed, the others were that also which Peter was *, but a primacy is given to Peter, whereby it is made clear that there is but one Church and one chair. So too, all [the apostles] are shepherds, and the flock is shown to be one, fed by all the apostles in single-minded accord. If someone does not hold fast to this unity of Peter, can he imagine that he still holds the faith? If he [should] desert the chair of Peter upon whom the Church was built, can he still be confident that he is in the Church? (The Unity of the Catholic Church 4 [A.D. 251]).
Cyril of Jerusalem*
Myth #1: First Among Equals
The first myth is that the Pope of Rome used to be “First Among Equals” (and/or “Ecumenical Patriarch”) and then “placed himself over the other bishops, wanting to be Head of the Church.”
FACT: The Pope NEVER held the title “First Among Equals.” However, he DID posses the titles “Vicarius Christi” (Vicar of Christ, late 300’s), “Servus Sevorum Dei” (Servant of the Servants of God, mid-400’s), and Yep, you guessed it, “Head of the Church” (late 400’s), a title by which the Pope is addressed, not only by innumerable Eastern Fathers, but ALSO by the synodal letters from THREE Ecumenical Councils (Chalcedon, Constantinople III, and Nicaea II). So, any Orthodox who denies that the Pope of Rome is Head of the Church does not stand with the Council Fathers.
As for Ecumenical Patriarch, that was an out-and-out creation by the Byzantine government in the 600’s (and it was never offered to Rome, but was designed for Constantinople). Gregory the Great was the first to deny this title to the P.of C. (calling it “haughty” and “unTraditional”) and the denials continued well into the 900’s (when Photius demanded to have it); and, after him, Michael Cerularius which was fuel to the fire re: the Great Schism.
Myth #2: Five Patriarchs with Equal Authority
The 2nd myth goes like this: “There used to be 5 Patriarchs, all with equal authority. Then, the Pope of Rome broke off from the Church, whereas the other 4 remained.”
Now,

this again, is not only revisionism, but out-and-out Greek bigotry. As stated, it makes it seem like there were 4 independent Patriarchs at the time who freely refused to stick with Rome in 1054. However, once one bothers to read the history, that’s not the case at all.
In 1054, the Patriarchs of Alexandria, Antioch, and Jerusalem were not the local bishops who used to rule from these sees (since all of the locals broke off with the Monophysites). Rather, the Orthodox bishops of these sees in 1054 were all Byzantine Melkites – Imperial appointees from Constantinople! Furthermore, they were presiding within Muslim countries; and their flocks were puny at best (most of the Christians in those regions being Monophysite, not Orthodox). So, they were no longer the great metropolitan sees of the ancient Church.
So, when the Orthodox say that there were 5 patriarchs and 1 broke off, that is not the case at all. It was not a 4 to 1 split. It was a 1 to 1 split – Rome and Constantinople. The sees of Alexandria, Antioch, and Jerusalem at this time (ruled by imperial-minded Greeks from Byzantium) did whatever Constantinople told them to do. And, if Churches like the Copts and the Jacobites turn out not to be Monophysite after all, then these men weren’t even the the legitimate bishops! But, the “Greek invaders” as the Copts and Syrians saw them.
bringyou.to/apologetics/a30.htm
I’m pretty sure the Patriarch of Jerusalem never followed the non-Chalcedonian Orthodox. In fact, I think the Council of Chalcedon raised the bishop of Jerusalem to the level of Patriarch.