In the year 1054, the Christian Church split into a Western Church and an Eastern Church. In this schism, or official separation, the church in the west became the Roman Catholic Church and in the east it became the Eastern Orthodox Church. Disagreements between the Western and Eastern Churches had been going on for quite some time. Most disagreements centered on the question of who had religious authority, the pope in Rome or the Byzantine emperor and the patriarchs (religious leaders of the eastern Christian church) in Constantinople. An early dispute erupted over the use of icons, or religious images. In the year 730, the Byzantine emperor, Leo III, banned the use of icons in Christian homes and churches. The pope disagreed with this and Pope Gregory III went as far as excommunicating the emperor. In 843 the ban was lifted, but the split between east and west had begun.
The power struggle between the pope and Byzantine emperors continued. The pope turned to political and military leaders in the west for support and began to cut ties with the Byzantine emperor. In the year 800, the pope crowned Charlemagne the new Holy Roman Emperor. This outraged the Byzantines who felt that the Byzantine emperor was the rightful ruler of the Roman Empire. The dispute between the pope and Byzantine emperors continued. The pope claimed authority over the church, kings, and emperors, including the Eastern Church and the Byzantine emperor. The Byzantine emperor claimed authority over the eastern patriarch and the church in the east. This matter came to a head in 1054. Cerularius, the patriarch of Constantinople, closed churches that used western rites. Pope Leo IX was furious and sent Cardinal Humbert to Constantinople to deliver a proclamation by the pope excommunicating Cerularius. Cerularius then excommunicated the cardinal, even though he had no power to do so. These actions showed that the schism between the Western Church and Eastern Church was complete.
I think that there are a number of different ways in which you might answer this question. I would suggest that you look and see what your book says or what your teacher has said -- they might have a different interpretation than mine.
To me, the first reason you could give for the schism is political. What I am saying is that the Roman Catholic church still wanted to assert power over the Church in the East. At the same time, the Church in the East felt it should not be subordinate since the Byzantine Empire was still going strong while the Roman Empire in the West had fallen. So it was partly an issue of each side wanting more power and local control.
You can also say it was a cultural issue as the culture of the East became more "Greek" while the culture of the West remained more Latin.
There were also issues of doctrine. One of the biggest was the "filioque" controversy. In this, the Eastern church objected to the Western church saying that the Holy Spirit proceeded from the Father and the Son rather than just from the Father.
The East-West Schism (split) of the Catholic Church was caused by cultural, geographical, and political differences. The beginnings of the schism dates back to as early as the division of the Roman Empire in A.D. 375 by Emperor Theodosius. He divided the empire into the Eastern and Western Roman Empires and moved the capital city from Rome to Constantinople (present-day Istanbul, Turkey). As a result of this division, an informal split within the Catholic Church took place leading to the formation of an Eastern Church in Constantinople and a Western Church in Rome.
This informal split deepened in the 800s when a series of disputes arose between the pope, the head of the Catholic Church, and the patriarch of Constantinople (also called the ecumenical patriarch), head of the Catholic Church in the East. The issue was the pope's authority over Christians in the East. Finally, in 1054, Pope Leo IX (1002–1054) issued an anathema (a formal curse) against the patriarch of Constantinople, Michael Cerularius (c. 1000–1059). The pope excommunicated (expelled) the patriarch and his followers from the Catholic Church. As a result, the Catholic Church was now officially split in two parts: the Roman Catholic Church in the West and the Eastern (or Byzantine) Orthodox Church in the East. Thereafter the Eastern Orthodox Church would accept the patriarch of Constantinople as the highest authority and would no longer recognize the pope. Members of the Eastern Orthodox Church followed the Byzantine rite (ceremonies); in the West, Roman Catholics followed the Latin rite and continued to regard the pope as their leader.
The capture of Constantinople in 1453 by the Ottoman Empire placed the Eastern Orthodox Church under Muslim rule until the 1800s. By the late twentieth century differences still remained between the Roman Catholic Church and the Eastern Orthodox Church, which now included the Greek Orthodox Church and the Russian Orthodox Church. However, the rift was somewhat healed in 1964 when Pope Paul VI (1897–1978) met with Ecumenical Patriarch Athenagoras I (1886–1972) in Jerusalem. The next year, each of the two religious leaders lifted the anathemas against the other's church.
Further Information: Bokenkotter, Thomas S. A Concise History of the Catholic Church. Garden City, N.Y.: Doubleday, 1990; Deedy, John. Retrospect: The Origins of Catholic Beliefs and Practices. Chicago: Thomas More Press, 1990; "Great East-West Schism." Encyclopedia Britannica. [Online] Available www.britannica.com/bcom/eb/article/5/0,5716,108295+16,00.html, October 20, 2000.
The Pope, Leo IX, wanted total power over the Church of the West, so he called a split between the two churches. Now, as you see, the Roman Catholic Church and the Eastern Orthodox Church are two completely different churches: the Church of the East remains traditional, whereas the Church of the West wants to be reformed; "modern", which isn't really a bad thing at all. Yes, as the person above said, they had their differences.
I am Christian (Catholic-Orthodox) half-half, so I am not bias.