The event that was MOST DIRECTLY responsible for increased tensions between Byzantine and western Christians was:
Crusaders attacked Constantinople on their way to Egypt. The sack of Constantinople in 1204 during the Fourth Crusade worsened the relationship between the Orthodox and Roman Catholic Churches and weakened the Byzantine Empire.
This event was pivotal in deepening the rift between the two branches of Christianity and had lasting repercussions for both the Byzantine Empire and relations between Eastern and Western Christians.