Nutshell:
Bishop of Rome (aka Patriarch of the West) had a position of honor among the other patriarchs. Whenever they met, Rome would be at the head of the table. Nothing more, nothing less.
But, somewhere along the line a pope got a bit pig-headed and decided that he has authority over all the other patriarchs, bishops, laymen and peons.
The East said "You're wrong".
One thing lead to another. An excommunication here, and excommunication there, a Crusade gone wrong and thus we end up with....
-Eastern Orthodox remain as we have since 33AD-ish.
-Rome keeps 'developing' and 'developing'.
If it ain't broke, don't fix it.