Check out this speech given by Pope Benedict XVI earlier this week. He quotes the 15th century Byzantine Emperor Manuel II Paleologus who was debating "an educated Persian".
"[The Emperor] turns to his interlocutor somewhat brusquely with the central question on the relationship between religion and violence in general, in these words: 'Show me just what Mohammed brought that was new, and there you will find things only evil and inhuman, such as his command to spread by the sword the faith he preached.'"Ok, so let us leave aside the incendiary content of the remarks and focus on who the Pope is quoting. Or, as my dad asked: "was not the byzantine emperor of the Greek Orthodox persuasion? Was he not a schismatic? Are his views ok [to be quoted by a Catholic Pope]?"
Well, I did a little reading on this. Manuel II Paleologus was in fact a Byzantine emperor, and as such was a member of the congregation of the Patriarch of Constantinople, not the Patriarch of Rome. The split between the two churches happened in 1054, and is usually attributed to a difference in language in the documentation from the Council of Nicea, but that took place in 325 AD, so it doesn't make sense that this disagreement waited 700 years before causing the schism.
In fact, the schism took place largely because of the advance of Islam. In the early church, and according to the first few convened Ecumenical councils, there were five patriarchs, all on an equal footing: Rome, Constantinople, Antioch, Alexandria and Jerusalem.
The last three cities were in Muslim hands by the turn of the millennium, so there were only two Christian power centers left - Rome (which followed Latin liturgy) and Constantinople (which followed Greek liturgy). So maybe the difference in language used caused some confusion over language of the Nicene Creed. But more importantly, with two power centers left, the balancing act was disturbed and conflict set in.
Another thing that the Eastern Church (and empire) was largely suspicious of was efforts by the West to resurrect the Western Roman Empire, by the likes of Charlemagne (who got official sanction by the pope in Rome, remember). Incidentally, Charlemagne was also a famous adversary of the Muslims (Roncesvalles and the Song of Roland etc.).
When the Great Schism happened, the Christians had lost all their Arab lands, but they had made huge gains in the Balkans, and still held all of Asia Minor. In fact, at the time of the Schism, the Byzantine Empire was at its zenith (in terms of geographic reach). But, within sixty years they were on the retreat again and had lost most of most of what is modern day Turkey to the Seljuks. They still held Constantinople though.
So, the Byzantines were quite happy allying with Rome during the Crusades (which began shortly after a major defeat of the Byzantines at the hands of the Muslim turks). They made many gains in the 1100s, and were back on top, so they resumed their fighting with Rome, which resulted in the Sack of Constantinople (by the western crusaders) in 1204, during the Fourth Crusade.
The Byzantines went back into a cycle of decline, and by the time of Manuel II Paleologus (who the current Pope quoted) the Byzantines had basically become like the late Mughals - emperors of one great city, and its outlying areas. He had in fact appealed to Rome on many occasions to try and seal the rift, but many of his own people (and the clergy in the hierarchy of the Eastern church) refused to accept such a reconciliation.
So, every time Byzantium was in decline, they would appeal to the West for help and every time they were ascendant, they would resume the fight with the west. In fact, hostility towards the west was a hallmark of Byzantium. Within fifty years of Manuel II Paleologus' remarks on Mohammed, the Byzantine empire was destroyed by the Ottomans. What's incredible, is that one of the Byzantine commanders during the Fall of Constantinople is said to have remarked: "I would rather see a Muslim turban in the midst of the City (ie, Constantinople) than the Latin miter."
Now, why is the Pope quoting a Byzantine? Well, I think for a number of reasons. One, it's a really incendiary quote. Two, it was made by an Emperor who was largely in favor of better relations between the Eastern and Western churches, so its probably ok to quote him. And three, Benedict XVI might be appealing to the folks of the Eastern Orthodox church to try and heal any rift, for a fight that he sees coming, and which the Eastern Orthodox chaps have been fighting for over a millennium.
Oh, and check out this graphic: Every time there is more pink on the map, there was a conflict with Rome. Every time there is less pink, there are frantic appeals to Rome for help.