Explain the two major disagreements that led to the great schism

If you're looking for doctrinal issues, here are a couple of the big ones:

The East objected to the addition of the Latin word "filioque" (meaning "and the Son") to the Nicene Creed, in which churches in the West confessed that the Holy Spirit proceeded from the Father and the Son (rather than from the Father alone, as confessed in the East).The West objected to the worship given to icons in the Eastern churches.

Those were key points of doctrinal dispute.  Ultimately, though, the struggle was over authority in the church.  in 1054 CE, there were mutual declarations of excommunication between the pope (in Rome) and the patriarch (in Constantinople) that  resulted in what is known as "The Great Schism" -- a monumental split between the western church (the Roman Catholic Church and what has become known as the Eastern Orthodox Church.   "Catholic" means universal -- the Roman pope was intent on asserting his leadership over all of Christendom.  "Orthodox" means "right teaching."  The Eastern patriarch and church were asserting their teachings to be right over against positions held in the West.  There were a number of doctrinal issues debated hotly between East and West over the centuries leading up to final break between the two halves of the church.  But more than anything, the split came down to "church power" -- who held control over the church.  

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