Failure to do this could take the form of an undirected relationship (two beliefs are "related" without either belief being the cause or the effect), or loops in a directed graph. I don't actually think we want to get rid of undirected relationships entirely -- people do use them in machine learning -- but I can't see any good reason for keeping the latter.

Feedback loops, where X affects Y and Y affects X, exist in real life, and you want to be able to model them.