Final answer:
The most significant event in creating Byzantine hostility towards the Latin Christian world was the Fourth Crusade in 1204, which led to the sacking of Constantinople and left a deep resentment among Orthodox Christians.
Step-by-step explanation:
The most significant event in creating Byzantine hostility towards the Latin Christian world was the Fourth Crusade. In 1204, the crusaders attacked and sacked Constantinople, betraying the Greek Christians and crusading ideals. This event left a deep resentment and strong anti-Catholic feelings among all Orthodox Christians. The Catholics established the short-lived Latin Empire of Constantinople, further damaging relations between the Greek Orthodox and Catholic churches.