At work, I'm surrounded by smart people. They often outsmart me but a common trap they fall into is not doing enough meta thinking. They seem stuck on level 1 of things.
And once you do that you will almost always moderate your statements, whereas those that think they are structurally in the right do not feel the need to do so, they will treat the rest of the world as though they're slightly stupid children and their tone will reflect that.
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.