I think in the real world everyone thinks they're playing chess and they can, more or less, tell you what the rules to chess are, and when asked they'll say they are playing their moves according to the rules of chess, but in reality they are not playing chess. They're all playing some other different game and often the players that are rewarded are the ones that won according to the rules of that game.

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.