Why is "schism" preferred over "demur" in this sentence?

Solution 1:

Demur as a noun is relatively uncommon, and I at least would consider it at least "dated". It means a pause, hesitation, but even that couldn't suit the context. Just my opinion, but I think the noun sense is rarely used except in the context of negation (accept without demur, there shall be no demur, etc.)

Demur is normally used as a verb today, meaning to hesitate, object, prevaricate. It's definitely not some "weaker" version of schism a split between strongly opposed parties, caused by differences in opinion.

In short, schism really is the only plausible candidate, regardless of whether the test writer forgot that demur can be used as a noun.