It's very common in philosophy (and the sciences, too) to find that the axioms lead to the wrong answer, and as a result say "oops, they must be wrong," and pick different axioms. In that case, though, the flow of epistimophlogiston is going from empiricism back to axioms, not from axioms to conclusions.
We as people both forward-chain and backward-chain. If I have principles that are important to me, I might reason forward from them to plan or conclude. And then if I discover an undesirable outcome, then that means I've learned something about myself, and then I can reason backwards to adjust what my principle actually is, and reason forward from that adjustment.
There's nothing morally wrong with learning and evolving. It doesn't by definition mean we're inconsistent.
Throw in some other logic, and you end up with the conclusion that the world can still be logical, but that many normative conclusions (which is what the world runs on) depend on moral axioms that differ from person to person.
So there's a distinction between people that reason correctly from their moral axioms, and people who don't. And among the ones who don't, there's a distinction between those that just make a mistake, and the ones that are deliberately presenting their arguments in bad faith. But even the latter have their own internal conclusions that are honest attempts at rational derivations from their internal values.