Things started to get dicey a couple of centuries before 1054, the traditional date of the split. For a few centuries afterward, it looked like the two groups might become reconciled, but none of those attempts lasted.
Human nature, pride, and "I'm right" all contributed.
In 1054 the Pope and the Patriarch excommunicated each other. The root of this particular struggle was over the West's use of unleavened bread, and the authority of the Pope over the universal Church. This particular conflict was predated though by issues over the foliage clause, and Petrine Primacy in general.
The Western Church (Roman Catholic) added the "Filioque" phrase to the Nicene-Constantinopolitan Creed, which violated the canons of the Third Ecumenical Council in 431, which forbade and anathematized any additions to the Creed, a prohibition which was repeated at the Eighth Ecumenical Council in 879-880 AD.
As Rudyard Kipling said, 'never the two shall meet'. As sure as the sun rises in the East and sets in the West, our habits, experiences and way of life are opposite to one another, and contrast too much for man to reconcile to both. He is either a Westerner, or he is an Easterner. The churches are the languages of each community, and help to govern the people in the denominations. Generally, the Roman church is acclaimed to have more power.
Take for example the burning of the Koran in Florida, which many bishops said was an act of freedom of religion in a democratic set up and therefore is legitimate. I too re comment it, for the Muslims should not allow the Koran to be used as cheap stuff to spread their numbers, but should keep it INSIDE their own mosque.
Christians, Catholics, Roman Catha and Greek or tho. Catha have all the same leader in Jesus, and so there are no differences in Jesus.
The process of estrangement of the Greek-speaking East and the Latin-speaking West developed over many centuries as Rome as the sole Christian authority in the West after the fall of the western half of the Roman Empire) grew slowly apart from the other patriarchates that continued in the eastern half of the Roman Empire for centuries, even as its territory was eventually nibbled away and finally all fell under Islam.
The most-cited date is 1054, when a representative (legate) of a pope that had died, whose death wan not know to the involved parties, excommunicated the Patriarch of Constantinople, who reciprocated not against the pope, but against the legate. There was never a mutual excommunication of the pope and the patriarch (the existing anathemas were rescinded late in the 20Th century), and relations continued, though strained. So that really isn't it.
Ultimately, the sack of Constantinople by the 4Th crusade in 1204 sealed the division, as it was clear that Rome did not consider itself "first among equals", but as the ruler of the Christian world. The Romans set up their own patriarch loyal to Rome, and ran Constantinople for about 50 years before a new emperor restored the Eastern Roman Empire and reinstated the Orthodox patriarchate.
Behind the pol ital maneuverings, though, was the innovation inserted into the Creed, the foliage, which the canons of the church prohibited. That and Rome's insistence on being the "one bishop to rule them all" made for a background of suspicion that the crusade sealed.
We pray for the day when the whole church can be united in faith and teaching.