A good general rule when socializing is never apologize. There is never a legitimate excuse:
1. Your screw up was accidental. You were oblivious to your situation when you shouldn't have been. Always give others the courtesy of paying attention.
2. Your screw up was intentional. Now you regret it. Why the bad behaviour in the first place?
I strongly disagree.
You can be 100% impeccable but you will inevitably enter into circumstances you can't possibly predict. Especially if you're very strong and wise, it's inevitable you'll step on lots of toes when you deal with others who are not as advanced, unless you first conduct very extensive anthropological, sociological and psychological investigations of the background of any group of people you would come into contact with, but clearly that would be absurdly inefficient.
Often when I say "I'm sorry" what I really mean by it is "I'm sorry you're too stupid to understand me", but I leave the last part out. It's true I'm admittedly frustrated with their lack of knowledge, however I easily distinguish between the dreary state of affairs of modern times where true knowledge is rendered difficult to grasp, and their failures to grasp it - the path of self-realization is indeed difficult, and at the end of the day I know nobody chooses to suffer, per the very definition of suffering, so I know the culprit is impersonal rather than personal, the culprit is not the person but ignorance and ignorance is as substantive as the void of space if you dig in the ground and that we call "hole"; ignorance is a state, not a thing.
Relatedly, if I never apologized, it would render my communication with others extremely difficult, because surely most people would not clearly perceive where I were truly coming from if I never apologized. They would think I was egocentric, insecure, dishonest or just plain dumb for not realizing when I'm wrong, and in my experience if you want to talk about serious things and converse in a piercingly direct way (as I prefer to do) then it's very important that your words carry a certain amount of credibility and integrity, otherwise the medium of your communication totally destroys the message.
Furthermore, why be concerned with how other people perceive you? Ultimately you should only be concerned with how you perceive yourself, however it's true on a conventional level it's also important how others perceive you. But - and this is the thing - I only ever feel that I've actually lost face if I error in my relationship with my own self, not in my relationships with other people. I do whatever the fuck I have to do in order to successfully navigate the conventionalities of modern society, to the extent the character and personality of who I am can withstand it, and I think if you can't stand to say I'm sorry to others then that's a pretty weak position. Or, if you just don't like people and you honestly want to be antagonistic towards others, then there are much more drastic measures you can take than just refraining to say sorry (and you may even want to say sorry in order to be properly passive aggressive or something).