Somebody might come across as arrogant because he can anticipate arguments other people come up with and understands their position better than they do, and disinclination to engage them from what is in the other guy's perspective an honest and satisfactory fashion could easily be interpreted as arrogance. I'm imagining someone like House MD (fictional evidence, I know). In such a case the "arrogant" academic might not perceive himself that way.
There is also the real life case of John Nash who IIRC others described as highly arrogant, but was nevertheless brilliant. He still had his capacity to produce useful work damaged by schizophrenia but that was probably due to genetic causes seeing as his son suffered similar problems.
Perhaps arrogance impacts different people differently? If you're brilliant to begin with, you may be able to do great work regardless of your arrogance, whereas arrogance in someone who is merely bright might cause a severe reduction in effective intelligence.
I have this belief that humility is a part of good critical thinking, and that egoism undermines it. I imagine arrogance as a kind of mind-death. But I have no evidence, and no good mechanism by which it might be true. In fact, I know the belief is suspect because I know that I want it to be true — I want to be able to assure myself that this or that intolerable academic will be magically punished with a decreased capacity to do good work. The truth could be the opposite: maybe hubris breeds confidence, and confidence results? After all, some of the most important thinkers in history were insufferable.
Is any link, positive or negative, between arrogance and reasoning too tenuous to be worth entertaining? Is humility a pretty word or a valuable habit? I don't know what I think yet. Do you?