The Great Schism happened because the church ( Chalcedonian Christianity at the time) developed different theologies in the West and East. The West was ruled by a pope, and the East was ruled by a patriarch. They had disputes over the origins of the holy spirit, whether to use leavened or unleavened bread in the Eucharist among others. There was a “Petrine Doctrine” that the East rejected but the West had accepted it. The Western half claimed to be the “mother of all the churches” as the pope wanted to be supreme as the Roman emperors did. It also modified the East’s Nicene Creed without their permission and they didn’t like that either. Both churches got to the point where they excommunicated each other! In more detail,
The seal of separation which was placed on paper in 1054, dividing the Church into East and West, was brought to a head by an innocent act by the Patriarch Michael Cerularius. He wrote a letter to Bishop John of Trania in Italy enumerating the innovations which had been introduced by the Roman Church, and he begged him to give this letter a wide hearing in order that the truth might prevail. This act apparently witnesses the fact that the Patriarch did not accept any sort of schism yet. Pope Leo IX sent a sharp reply, severely rebuking the author of the letter.
The Emperor of Constantinople, Constantine Monomathus, facing a threat of his political interest in Italy, had need of the Pope’s help, and he sent a conciliatory reply asking him to send delegates to restore friendly relations. The Pope sent Cardinal Humbert with a different mission, which he fully executed. Humbert did not meet the Emperor or the Patriarch, but he laid on the altar of the Church of Saint Sophia in Constantinople a bull of excommunication against the Eastern Church, attempting to stigmatize it as “the repository of all the heresies of the past”, and then hastily disappeared. The Patriarch in turn drew up a sentence of excommunication against the Western Church, signed jointly by the other Patriarchs. And thus the black seal kept closed the gates of the bridges between East and West. (Believe: Religious Information Source Website)