Alright so I've had some long and windy discussions about everything related to ego and arrogance. Most of the time I've concluded that I really dislike arrogant people. I'm not really sure why though. I think it's probably because they place themselves above you and that is interpreted as a personal attack. It's really the claim that somehow you're less important than they are.
Usually what I really want is to see the arrogant person person fail at what they're so proud of. On the other hand, if there are people who really are good at what they do, they don't brag about it and still have respect for people you don't get the same kind of urge to see them fail. Quite the contrary, you want to see them succeed. So ultimately I wonder if the deciding factor is the person's opinion of others. In a sense by not bragging about themselves they still let you be on equal level -- simply by being yourself. You don't feel judged based on your skills but by who you are as a person.
Having said that, I still feel uncomfortable around arrogant people. Rationalizing about it doesn't help. I have heard some people say that arrogant people are just insecure and crave for attention. That may be, but I'm not sure why it comforts people to hear that. It's as if by knowing that the arrogant person has problems which result in him trying to be better than other people it somehow makes the argument of other people being at a lower level moot. It's probably because then everyone knows that he's formed his opinion for the wrong reasons -- he's somehow failed and as a result he has this delusional view of others.