Is it rational to be insulted?

Somebody recently said something somewhat racist that insulted me, and after I got over the initial shock and anger, I began wondering exactly why people are insulted; Shocked, maybe, but why insulted? What does the feeling really mean? Wouldn’t the rational thing to do be just to shake it off and be annoyed; What is the difference between being insulted and being angry or annoyed?

I am curious to find out what exactly being insult means, what it is, and why we feel it. Is it rational? What do you think?