Yes, agreed. While I have known some very smart people who were arrogant, I think, contrary to what a lot of people are saying here, that intelligence and arrogance are actually orthogonal. There are plenty of people in the world who are not so smart and are still arrogant. Arrogance is an emotional problem, not a natural function of intelligence.

While your definition of arrogance is not bad at all, I will offer a variation: refusing to consider the possibility that one might be wrong.

I used to be one of those smart, arrogant people myself (arguably smart, anyway; certainly arrogant). I have found the conscious practice of humility to be very valuable.