1054, in fact, but the 1204 ransacking of Constantinople certainly didn't help with how the "Franks" (because that's how the Catholics were mostly called) were seen by the Christian-Orthodox (if it matters I'm a Christian-Orthodox myself).
I was reading a travelogue written by a Russian monk (? not sure, either a monk or a wealthy boyar predisposed to the Holy stuff) who was visiting Constantinople sometimes in the early 1300s, so a century after the whole tragedy, and he was still describing how destroyed the city looked because of the Franks and what big of a tragedy that was.
If you read Wikipedia, there was the Massacre of the "Latins" in Constantinople in 1182. That almost certainly made it easy to make it a revenge play for the Venetians and associates.
What I find most interesting is the Romans were unbeatable in battle, even the Byzantines. However, maintaining a large military presence was expensive and politically difficult to manage. So they used annual mercenaries from the north for the usual frontier squabbles, and the main army did the heavy lifting. It fell apart when there was a major conflict, and didn't help that the army held the city hostage demanding more money. So everyone was corrupt it would seem. Also there were the persistence of rumors of knights that may have kept most of the treasure for themselves and headed off to Cyprus. The Knights Templar were insanely wealthy given the times and cost of resources to mount expeditions.
They were, though? Adrianople, Yarmoud, Manzikert, Myriokephalon etc. it's just that the empire was extremely resilient and was generally able to recover from disasters which would have led to the collapse of most other states.
I think Hannibal is owed some credit for marching elephants over the alps - I believe Rome razed and erased Carthage on their 3rd or 4th try? No matter really, it wasn't their 1st.
By 1200 the Romans had been beaten in battle many times. Their loss at Manzikert to the Turks in 1071 severely weakened the empire, and they never really recovered from it.
It's funny how the Battle of Manzikert went from being an obscure battle only a handful of scholars cared about to a major topic in popular consciousness.
It's actually not quite so clear cut. 1053/1054 was when mutual excommunications between Rome and Constantinople happened, but (as the schism itself is evidence of) Constantinople did not speak for the entire church, and other eastern sees continued communion with Rome for quite some time afterward.
It really wasn't obvious at the time, though and it took at least 100 years or more for the split to become permanent.
e.g. There is currently a schism between the Orthodox Church and the Russian Orthodox Church which technically is not that different. Does that mean that the Russian Church is no longer Orthodox?