If relevant Anastasia, Theopedia lists some of the factors that led to the 1054 split as the following:
- the insertion of the filioque clause into the Nicene Creed by the Roman church in direct violation of the command of the Council of Ephesus, an action called non-canonical by the Eastern church.
- disputes in the Balkans over whether the Western or Eastern church had jurisdiction.
- the designation of the Patriarch of Constantinople as ecumenical patriarch (which was understood by Rome as universal patriarch and therefore disputed).
- disputes over whether the Patriarch of Rome, the Pope, should be considered a higher authority than the other Patriarchs. All five Patriarchs of the One Holy Catholic and Apostolic Church agreed that the Patriarch of Rome should receive higher honors than the other four; they disagreed about whether he had authority over the other four and, if he did, how extensive that authority might be.
- the concept of Caesaropapism, a tying together in some way of the ultimate political and religious authorities, which were physically separated much earlier when the capital of the empire was moved from Rome to Constantinople. There is controversy over just how much this so-called "Caesaropapism" actually existed and how much was a fanciful invention, centuries later, by western European historians.
- certain liturgical practices in the west that the East believed represented innovation: use of unleavened bread for the Eucharist, for example. Eastern innovations, such as intinction (dipping) of the bread in the wine for Communion, were condemned several times by Rome but were never the occasion of schism.
This conflict led to the exchange of excommunications by the representative of Pope Leo IX and the Patriarch of Constantinople, Michael Cerularius, in 1054 (finally rescinded in 1965) and the separation of the Roman Catholic and the Orthodox churches, each of which now claims to be "the One Holy Catholic and Apostolic Church." It should be noted that at the time of the mutual excommunications, Pope Leo IX was dead. Therefore, the authority of Cardinal Humbertus, the Pope's legate, had ceased; therefore he could not legitimately excommunicate Patriarch Cerularius.
The final breach is often considered to have arisen after the sacking of Constantinople by the Fourth Crusade in 1204. This Fourth Crusade had the Latin Church directly involved in a military assault against the Byzantine Empire, Constantinople, and the Orthodox Patriarchate. The sacking of the Church of Holy Wisdom and establishment of the Latin Empire in 1204 is viewed with some rancor to the present day. In 2004, Pope John Paul II extended a formal apology for the sacking of Constantinople in 1204; the apology was formally accepted by Patriarch Bartholomew of Constantinople.
Source:
Great Schism | Theopedia
I think the Caeseropapism one, and the factors of East and West already being split politically into two halves by Emperor Diocletian in 285 AD. To me personally, this would explain the insistence from the Rome to recognize the Pope as Spiritual Head of the Church on Earth. In this mindset, it would be "Rome was head of the Empire, while the Empire has fallen, rome has not and our Pope is the one thing that ties the rest of the old Empire together.