Arrogance (n) : overbearing pride evidenced by a superior manner toward percieved inferiors - in other words, arrogance can also apply to an instance when someone is overbearingly proud about his/her most humble behaviour and in thinking how much more humble he/she is compared to the inferior others with arrogance. Arrogance is simply a view of one's self inwhich you think higher of yourself in a certain respect - as in: "I have accomplished more self-depreciation than you have, whaaa!"
Two of the greatest artists, Michelangelo and Da Vinci was utterly arrogant in their dealings with each other, other fellow artists and normal people, yet they did not cease to be one of the greatest geniuses ever. In fact, Michelangelo is generally seen as the greatest artist ever. Arrogance means nothing in itself, some people can tollerate it, others can't. The great composer Beethoven - another emminent genius, was also arrogant - he even said in his own words that his behaviour is justified because he is Beethoven - there was 20000 people at his funeral!
Arrogance is a personality trait, so what?
Socrates was arrogant himself when he said: "I am the wisest man alive, for I know one thing, and that is that I know nothing."
Because, there is arrogance in utter self-depreciation, just like altruism is selfishness at bottom: it's attention-seeking in essence - it's a sort of exhibition of "wow, look how humble I am!"
Ultimately it is a meaningless concept.