One of my kids is extremely frightened of bugs. As in, if there's a fly/mosquito/bee in the room - far away from her - she will freeze up and refuse to move. If she's in small proximity, she gets uber-distressed and starts screaming.
She is OK with butterflies or small fruit flies though, and interestingly enough, is much more OK with spiders (she's not as spider friendly as my other kid or myself, but they don't send her into a screaming fit and she isn't scared to approach and look at an interesting spider).
Part of that is, IMHO, absorbed from her mother who's deathly afraid of pretty much any bugs. But she's clearly not simply aping her mom, because of aforementioned spider thing: mom is MORE afraid of spiders than any other bugs .
What are good approaches/strategies to lessen fear of insects in a child?