‘Arrogance’ comes from ‘to arrogate’ — to seize. The opposition to arrogance (from the social-minded people) is the opposition to anyone “autocratically” claiming “rights” — especially, the right to not notice others!
I have always liked seeing it, specially in women — when rightly done! In the good arrogance, a woman, say, ignores you because she has no reason to notice you! If there is weighing at all — there ought to be a judgement. And the judgement must be grounded on decent factors. Moreover, there must be a weighing before rejection! (If there is no weighing at the moment, it is ok, for maybe the person was busy then.) This is healthy. You remain open for “new business”, new influences, new ideas and opinions, but you keep a tight control over who is allowed to pass in too! (Also, it may be possible to create a beautiful world too, by noticing only the beautiful parts of the common world, and declaring the other parts to be “of no consequence and therefore to be harmlessly ignored”. I have not succeeded it in.)
In the bad arrogance, the person feels complete and secure in what he/she has — “family and friends”, and has no interest in “random others”. It is bad because it is ugly to watch, and unhealthy. Humans ought to be “open”! Humans ought to be “moving”. The bad arrogance is ugly because it suggests a “halt” in living.
The socially-minded people do not make the above distinction, and condemn all arrogance.
(For completion: there is a place for kindness too, even towards those you choose not to notice.)
I have been struggling with the issue for at least a decade and half now. What has bedeviled me is the question why, when I like or (in some circumstances) love arrogance in others, do I not inculcate it in myself? Even on the streets, I notice well-dressed women out of politeness, because Heinlein says it is polite. (This is mad, I know.) In general, I essentially keep judging everyone anew all the time!
I understand the reason now. I hate hurting others, and arrogance hurts many people. (People like to be noticed — for what they are, how they are.) (Though, to me, being on the receiving end is invigorating! When I am in good mood, the idea is, “fine, ignore me — let me earn the concern”.)
The only way I see out of the trouble is somewhat harsh to hear: One must be prepared to be brutal. In many cases, the choice is simply between hurting oneself and hurting others. Even though hurting oneself may seem cheaper, for the sake of yourself, you should choose hurting others!