What if we humans don't use logic at all?
In linguistics, there's a term "thinking for speaking" - it is involved in a hypothesis that there is no language of thought - that we only ever "think in language" when we are thinking about speech or text.
What if we also don't order our thoughts into logical progressions unless thinking about it? This would seem to be a subset of "thinking for speaking" - a "thinking for arguing".
And it would leave our actual thought-forming process entirely opaque, unexaminable, insofar as anyone can dream up premises to support any given outcome, with no regard for whether these premises had any role in forming the opinion in the first place.