What disagreements led to conflict between Catholic Europe and the Byzantines?

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From the book APOSTOLIC HISTORY OUTLINE by Marvin M. Arnold, D.D., Th.D.

AD 707-741. Emperor Leo III ruled. The Byzantine Emperors (Eastern catholic) brought widespread terror. In Italy, image worship was a fact. (Bernstein & Green, page 149)

AD 707. Muslim armies besieged Constantinople. Muslim killed catholic; catholic killed Muslim. Rome's religion was mocked. Muslims called it idol worship and royalism. The term Political popes was heard. (H. Trevor-Roper, page 84; S.P. Wachs, Judaism, page 19)

AD 726. Byzantine Emperor Leo III forbad image worship. A big fight started. Western Catholicism wanted images. Icons were and are images. Iconoclasts (critics, dissenters) broke up images. Iconolatry remained, and in 787 the Nicaean Council approved of images, crosses, beads, relics. (Bernstein & Green, page 156; O.W. Heick, page 235)

AD 867. One pope anathematized another; there were popes and anti-popes. Western catholics of Rome fought Byzantine catholics. The Vatican, in time, dominated.

There were Byzantine political and theological woes. (Langer, page 248) Monophysites of Syria were butchered by Rome's party but many fled into Muslim territories for protection.

AD 1124. There were 2 popes at once, and they were Honorius I and Celestine I. Pope fought pope. (William Langer, page 215; See D.A. Yallop In God's Name, Bantom, New York 1984) Rome's catholic party tried to commit genocide against Byzantine catholics!

AD 1202 - 1204. The fourth crusade. Rome's crusaders took Constantinople and Western catholics were massacred by Byzantine catholics. (Bernstein & Green, page 226; R. Bainton, pages 205, 210, 212; Lachs & Wachs, page 21)