I've been thinking about the function of apologies and come to some conclusions. Though it may be helpful for me to run this by an external perspective, because I fear my thinking may be one-sided.
I presume most are familiar with the general principle surrounding apologies, taught to us at school implicitly or explicitly:
If you have done something wrong, you must apologize, and reassure whoever's affected that you won't do it again. Not doing so would be to run from one's responsibility. Conversely, do not apologize when you have done nothing wrong. This undermines the significance of apologies and reduces them to a hollow, kneejerk platitude.
As I grew older, I became increasingly aware of a caveat, whether explicitly stated or not.
Sometimes apologizing when you have done nothing wrong is justified, for example to keep the peace.
If I had to guess, I'd say 60-70% of people probably accept this caveat in mild cases. And 99% accept this caveat in extreme cases. An extreme case would be one where some violent psycho is demanding an apology. So giving one may be worthwhile just to protect yourself in the short term until you can escape. A milder case may be one where you genuinely cannot see what you have done wrong, but the short-term utility in giving an apology to preserve your relationship outweighs the long-term damage done to the value of apologies in general. I think one convincing case may be a working relationship you do not care much for but could become a major source of stress if you don't swallow your pride and make peace. You may damage the long term value of apologies, but you risk damaging many other long term things if you don't say sorry!
However, I have become increasingly aware of another caveat.
Sometimes it is simply not worth apologizing, even if you have done something wrong.
I wouldn't be surprised if a majority of people refused to publically accept such a caveat in a mild case. I wouldn't even be surprised if a significant portion of people reject the caveat in the extreme case. However, I have gradually come to the conclusion that this additional caveat is also acceptable, even if I would certainly never tell a small child such a caveat. To explain my reasoning, allow me to list the three things that give an apology value in the short term, as I understand them:
1) It reassures the apologee that the one apologizing will make an earnest effort to change their ways.
2) It serves as a verbal admission of wrongdoing, which will urge the one apologizing to change their ways.
3) An apology has intrinsic value in the short term, via. the principle of apologies. (I think there is a philosophical term for the intrinsic value of good acts independent of the utility, but I cannot be bothered to find it).
I have made the very obvious observation that there are many circumstances where 1 and 2 might both not apply. There are many circumstances where apologizing offers no reassurance to the apologee, or motivates the apologizer. Leaving the only reason to apologize being a commitment to the principle itself or the abstract long term damage done to apologies in general by not apologizing. Suppose one has an "evil" and incompetent boss, and you have made an error at work. In such a situation, suppose apologizing would only make your boss aware you even made a mistake and the evil boss will bully you to a highly unjustified degree. Or perhaps there is good reason to believe that an apology will be taken as weakness - that rather than receiving forgiveness or a bounded, proportionate punishment, the person/people who perceive the wrongdoing may feel vindicated in ostracizing you or inflicting a wildly disproportionate punishment. I think about this in the context of "cancel culture". You may have made a comment that was legitimately mean or offensive 5 years ago, but if apologizing feeds the mob and potentially damages your future, I think it's more pragmatic to remain dead silent and quietly resolve not to repeat the same mistake.
In case you are wondering, these thoughts were not spurred by some particular wrongdoing I have committed (lol). I think now that I'm far outside of the sheltered world of school, I see many circumstances where such conditions may apply. We work rather hard to create an environment for children in the developed world where they are forgiven quickly and consequences for their wrongdoing do not have far-reaching consequences on their entire life. So giving them an idealistic approach to apologies is good and may instill principles. Yet in the modern world, where forgiveness seems to be turning into an exceedingly rare commodity, it simply doesn't make sense to engage in total, naiive good faith with many situations. If forgiveness loses value, so does apologizing.
Does anyone have any thoughts on this? Is the first caveat / second caveat obviously true or obviously false? I am compelled to share this in case I am missing something obvious. Perhaps my 3 short term reasons in favour of apologizing are missing some obvious 4th item, or I'm downplaying the long-term consequences too much. I have several other thoughts about the nature of apology that don't feed into a particular point above, but somehow also feel relevant:
One other aspect of apologies is they can totally change how a blunder is perceived by others. If one puffs their chest out and insists they do not owe an apology, or made a blunder but "have no regrets", that can exert a shocking amount of influence on how the people around them perceive their wrongdoing. In this way, right and wrong become subject to interpretation to an extent - an interpretation you also exert influence over. This all sounds very manipulative, but if simply reframing a situation can absolve you of most or all of the blame, did you even do anything that bad in the first place? Perhaps you're being too hard on yourself? In some situations, the answer is probably yes. And if a stubborn insistence on one's own innocence feels like it goes too far, simply neglecting to bring it up can move the needle a shocking amount, as can those slimey pseudo-apologies where a wrongdoer expresses sympathy while tiptoeing around acknowledging any wrongdoing.
Apologizing or an apologetic stance can also be self indulgent. A way of trying to quickly pacify people, or an indulging in one's own insecurities about one's own shortcomings. People of such inclinations would probably benefit from actively considering whether they have done something wrong, and whether they would expect an apology from someone else who had done something similar in their position. And focussing on rectifying a situation or preventing it from reoccuring is undoubtedly much more important than the apology, noble though it may be.
Lastly, I should point out the very obvious point that an apology is much more than a "sorry". One can give a very sincere apology without ever uttering the word, while a "sorry, but" can be anything but an apology lol. I shall define an apology as, fundamentally, an admission of wrongdoing.