Have you ever spoken with a developer who you thought was arrogant? It's hard not to find at least one person that you work with that doesn't give off a condescending air.
I had always wondered where this comes from, if my field just so happens to enforce this kind of behavior or if maybe the field just attracts a certain kind of person. I had a talk with a friend of mine a while back who had noticed something similar. What's more is he had noticed it coming from himself when talking with junior developers or sometimes people new to the team. As we were talking about some of the situations that came up, we realized what the source was.
You know nothing
The depth and the broad range of subjects within the field tends to influence this kind of thinking, but moreover, coming off as arrogant actually comes from a self-esteem problem. My friend and I realized that when we came in to the field, we were surrounded by people who knew much more than us, we are constantly reminded that no matter how much we know, it is a drop in the bucket.
Here is the kicker, if you always think that you don't know anything, when you meet someone who knows less, there is a knee jerk reaction to say something in the lines of "How could you not know that?" Of course, what you are really saying is, "I know so little and I know that, how do you not know that?"
So that was what he was feeling and of course something much worse gets communicated. I'm not really sure how to fix the problem where developers feel like they know nothing, but I know that its important to try to have a different reaction when dealing with those who are seeing or realizing what you already have for the first time.