We should ask ourselves the question "what would I still believe if this factual claim turned out to be wrong?". If the answer is "the same thing" then perhaps that means the fact isn't really our underling reason for the belief. At that point we should try to argue from the underling values directly, if we understand them, and sometimes we don't.
If, instead, the answer is "I'd change my mind" then the fact really is your reason and the argument is more reasonable, but we should still try to understand our values.
Perhaps asking that question consistently of ourselves, including in areas we feel most certain, is harder than it sounds. Perhaps we don't notice when we're arguing a fact as a proxy for our values.
It does sometimes feel extremely uncomfortable to state our values directly. Why is that? Often I think others will think I'm mad if I do. Perhaps I need to try harder.