Apologies make sense when your predictions are imperfect and there is uncertainty around your hidden brain state. So, often. An apology lets the recipient know

Apologies make sense when your predictions are imperfect and there is uncertainty around your hidden brain state. So, often. An apology lets the recipient know the fault didn't lie with your objective function, but with your predictions. It also signals to the recipient that you care about them. Examples: -You make a joke that offends someone when your goal was to make them happy not offended -You make a mistake at work that you thought would save everyone time but now causes someone else extra work -You accidentally knock someone down while playing sports In all of these examples you had a friendly objective function that because of imperfect prediction resulted in an unfriendly outcome. An apology tells your victim that the pain you caused them was accidental, not purposeful, and reassures them that you care about them and will exert effort to not hurt them in the future. These are things worth saying because otherwise the apology recipient may not know. P.S. I am sorry you are being downvoted. You laid out your thinking and asked for examples that could change your mind. I find that pattern commendable.