For some people, arrogance is indeed a defense mechanism. A person does not want to be found wrong, questioned or debated so he becomes arrogant.
For others, it is a natural part of their personality. They believe they are always right, know all the answers and feel there is no need in arguing with him.
The difference in the first case, the arrogant person knows he does not know everything, may not be right, etc. but does not want anyone else to know that, thus his insecurity leads to arrogance.
In the second case, the person is never aware or considers the possibility that he may be wrong, or not have all the answers and his persona projects an arrogance that most do not want to deal with, so they listen and ignore.