I've heard that when Bugs Bunny was first shown eating a carrot, he was impersonating a popular movie of the time. People of that time got the "joke," and he just kept eating carrots.
In time, that movie has been forgotten, and now people associate carrot-eating with Bugs Bunny.
And the moral of the story is: rabbits don't eat/like carrots normally, but they are given them because Bugs Bunny likes them.
Is it true that he was impersonating someone? If so, what was the movie called?