It has less to do with theology than it does with politics. This is about to get lengthy, but remember: you asked for it!
The Catholic view is that the Bishop of Rome (the Pope), has jurisdiction over the entire Church. The Orthodox view is that there was more or less an equality between the Bishops of Rome, Constantinople, Antioch, Alexandria, and Jerusalem. This dichotomy had been developing for centuries. Early Patristic literature will reveal that the earliest Church viewed Rome as the headquarters of the Church, and that this view goes back to as early as 96 AD.
However, the Roman Empire was in fact two distinct spheres---East and West. As Christianity gradually became legalized and more a part of the cultural structure, it, too, reflected this difference. In the West, people spoke Latin; in the East, they spoke Greek. You had two sets of Canon laws, two sets of dates for the celebrations of Christmas and Easter, two different versions of the Nicene Creed. After about the 11th century, when the Pope tried to exert authority over Eastern bishops, they resisted him on the grounds that he was exerting authority that did not belong to him. The West saw the East as not adhering to the ancient patterns of authority that Jesus established with Peter and the Roman See.
Again, this was a long, gradual separation; it took about a thousand years for the real friction to begin, and that had a lot to do with culture, once again. In the East, you had "Byzantine" Christianity, what we now call Orthodox; it was based on the Greek liturgy and was heavily influenced by the Eastern Emperors. In the West, you had "Latin" Christianity, which, after 476, wasn't influenced too much by the Roman Emperor since there
wasn't any Roman Emperor. There had been cooperation between the Bishop of Rome and the Emperors in the calling of the first eight ecumenical councils; but now, there wasn't any Emperor, and when the 1st Lateran Council was called by Pope Callistus, only Western Bishops attended.
(It is worth noting that between the years 314 and 655, out of the Sees of Rome, Antioch, Alexandria, and Constantinople,
only Rome never had a heretical bishop. [In fact,
no Bishop of Rome has ever taught heresy.] In the years 512 and 639, all three of the Sees other than Rome had Patriarchs which were Monophysites and Monothelites; at other times, they were Arians or Nestorians.)
The whole thing came to a head when the phrase "from the Son" was inserted into the Nicene Creed at the Council of Toledo in 589. The Eastern Bishops preferred the wording "through the Son", and they did not understand that the wording at Toledo was chosen to combat a heresy in the West at the time; to them, it simply seemed as if the bishops of the West were ignoring the East's concerns. In reality, it was probably a case of both sides totally misunderstanding the other.
Did anybody doubt that the Holy Spirit came from both the Father
and the Son? Probably not, but that wasn't the point. The Eastern Church viewed the West as meddling with the Creed, while the West viewed the East as refusing to acknowledge the supremacy of the Roman See. The divergence developed further from this point onward.
The final split probably would have come about anyway, but the two principal actors in the drama certainly didn't help things any. An ailing Pope Leo IX had ordered all Greek-rite churches in Italy to adapt Latin-rite liturgies. The Patriarch of Constantinople, whom I'll discuss in a minute, retaliated by ordering all Latin-rite churches in Constantinople to adopt Greek liturgies. The Latin-rite churches refused, and the Patriarch promptly shut them all down, and wrote a letter to the Bishop of Trani in which he castigated all Latin-rite practices on no uncertain terms. This letter, or a copy of it, was passed on to Rome; the Pope was outraged.
At this point, a couple of provincial couriers from Constantinople showed up in Rome, bearing letters from the Patriarch to the Pope. In them, the Patriach had addressed the Pope as "Brother" instead of the customary "Father", and he had signed it "Ecumenical Patriarch", which the Pope and his cardinals construed as meaning Patriarch of the whole Church, East and West. Actually, use of the Greek term
Oikoumene, at least insofar as the Patriarch of Constantinople was concerned, meant only the Byzantine Empire, but the Pope's legates didn't realize this.
The Pope sent his secretary legate, a guy named Cardinal Humbert of Moyen-Moutier, to Constantinople with a letter condemning the Partiarch for his upstart usage of the term "Ecumenical Patriarch", and criticizing his closure of the Latin-rite churches within his jurisdiction. The Pope couldn't have made a poorer choice of whom to send; Humbert didn't speak Greek, had no use for the Byzantines, was hot-tempered, and was a career ladder-climber in the Roman Curia. On the other hand, the Patriarch, a guy named Michael Cerularius, was no pearl either; he had spent most of his career as a civil servant, had no training in diplomacy of any kind, had no use for Latin liturgy or the Papacy, and was ambitious, unsubtle, and more than a tad arrogant.
The irritated Humbert was not received with open arms in Constantinople, and this annoyed him further. Deprived of the customary diplomatic niceties, he in turn shoved the letter from the Pope into the Patriarch's hands without so much as a hello. For his part, the Patriarch couldn't believe that the Bishop of Rome would dare to address him in such a manner, and decided that Humbert and his legates were therefore phonies; he refused to accept them as legitimate representatives from Rome, curtly dismissed them, and refused to have anything more to do with them.
This sent the Romans into transports of rage. They stayed in Constantinople for a while and were received by the Byzantine Emperor, who treated them kindly and urged them to try to work things out with the Patriarch. The Patriarch continued to ignore them, however, and finally, on Saturday, July 16, 1054, Cardinal Humbert barged into the Church of Holy Wisdom right in the middle of Holy Mass, and slammed a letter down on the main altar excommunicating the Byzantine Emperor, the Patriarch of Constantinople, and all their followers, and departed, actually wiping the dust from his feet as he did so. Whether or not Humbert actually had the authority to make this move is questionable, but he made it anyway, and the Patriarch replied in kind by excommunicating the Pope and all Latin Christians, and the break was complete.
The whole thing can be attributed in large part to egotistic personalities and the regional politics of the period; there were underlying religious differences, of course, but it really shouldn't have come to the break that it did. Both sides made mistakes, and both sides totally misunderstood the other. The mutual excommunications were lifted on December 7, 1965, by Pope Paul VI and Patriarch Athanagoras I.
I realize this is a long post, but I have only barely touched the surface of the Eastern Schism; is you ever decide to examine the depths of the politics behind the whole thing, you will find them fascinating; we don't have the term "Byzantine" (meaning labarinthine complexity and devious intrigue) for nothing.
Hope this helps.
---Wols.