It would be interesting to read a similar essay about how some people mistakenly think reasoning is about truth finding. That would be closer to the realizations I've had.
Personally, I find reason to be the only way to find truth.
Mathematics isn't concerned with deciding the 'true' axioms, instead they explore what happens if you (say) grant/deny the axiom of choice.
Go write the essay if you've had fun realizations!
Which is to say that no one thinks they're irrational or unreasonable. But that's also part of the game. For many people the real game is social, not truth-finding, because that's where the real stakes are. I don't think people are explicitly aware of it, but they learned that this is the way the game is played because that's what everyone else is doing, frequently even the truth-finders. And again the real stakes are here, and anyway it comes more naturally to most people. The truth-finding game is hard and often has worse prizes.
Is this a matter of semantics? It's strange because, if a word's meaning comes from how it's used by most people, well what most people say and believe reasoning means and what they are actually doing when they say they are reasoning are different.