Why was there a conflict bewteen the Holy Roman Empire and the Roman Catholic Church?

Tensions, disagreements, rivalry and contradiction were in the making for several centuries until the Great Schism of Christianity occurred in 1054. There were disagreements over theological doctrines, over the celibacy of priests (the Orthodox didn't support it), over due authority (primacy of Rome or Byzantium? A question with political consequences), etc. The Roman Catholic Church used Latin as the official language and a good part of its norms and regulations were founded on Roman law. Meanwhile, the Eastern Orthodox Church based in Byzantium used Greek as the official language and its theology and doctrines were influenced by Greek philosophy.