When it's "not your fault" apologizing hurts your pride. Apologizing when you don't feel at fault can feel like a lie, but part of what you're doing is humbling yourself before that person, saying that you choose them more than your pride. Non-english speaking cultures have this baked into their linguistics. Japanese comes to mind.

A lot of these AITA posts could get solved when the OP of the post just apologizes to their partner/friend/family regardless of who is at fault. You may be right, you may die on your righteous hill, but you're going to lose that connection no matter how right you are.

"Being right" and being right isn't always the same thing. Sometimes it's better to say "I'm sorry, you're right," and choose their feelings over your own.