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So what happens when different churches are established and have different words passed down?
well, there weren't different churches established, with different passdowns. just one deposit of faith.
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This (the schism) all comes down to authority. Who (or what) is ultimately the authority of the church? The bread was just a symptom of this authority battle.
it isn't as simple as that, unfortunately. the short version is that there were two things going on - one an desire for conformance, the other a move to reform. they were related.
the desire for conformance due to geopolitical realities is not new and has always been "a thing" in Christendom. this is a driving factor behind the first ecumenical council, for example - many of the councils, actually. thats why many of them were called by emperors. in a time where the aim of the state, the philosophical concept of the Good, was derived from the faith of the people having a misalignment was a huge problem. the issue in the ~8th century was that the overarching empire fell, and the desire for conformance became local (within the Carolingian empire, for example). So you had this conforming pressure that wasn't unified. it forced conformance
and change on only one part of the church. since it was only one part, the church
as a whole did not resist (or adopt).
secondly, and really also a consequence of the collapse of the roman empire, was the local subjugation of a bishopric to the local feudal lord in the west. the same kind of desire for control was there, but at the local level if plays out more in terms of corruption than in control. this lead to a big issue with simony, the purchase of a bishopric, because it was connected to power and wealth. the reaction to this was a desire to fix it, and the only way to "fix" a bishop is with some higher authority. there is no such higher authority in a singular way in the east - you can only get several bishops together collectively to depose a bishop.
both of these lead to a centralizing movement, and that is what you got - around the bishop of rome. this centralizing became stronger and stronger, until it was turned against the east, which resisted it in both paths. it resisted the conformance at odds with tradition (the filioque, unleavened bread) and resisted the centralizing power in the papacy.
together they lead to the schism.
the thing is, though, we have the benefit of a historical vantage point in a way people in earlier centuries did not. unlike the carolingian court, we
know that the filioque was novel - they apparently seemed genuinely convinced it was authentic and the east had changed it. we
know that the east and west both used to cross themselves the same way. we
know that both east and west used leavened bread. and so on.
we can only be accountable for our own decisions, based on our own inheritance, not for those of the past.