Good question. It's more of an aesthetic reason that we're accustomed to seeing in society. Hairlessness is seen is "feminine." In the US, as shorter and more revealing dresses become popular in the 20th century, shaving was encouraged for women. In fact, businesses selling shaving supplies attacked women with armpit hair, calling armpit hair "unsightly" and "a problem" so that women would buy their products. Some ads did use the excuse of hygiene though.
Over time, it's just expected that women are hairless. However, men do shave as well (besides facial hair), but mostly for athletic reasons. Men who shave for aesthetic reasons are usually those who build muscles or model.
@nabeelplus and LifeMeansChange - I agree that the practice of shaving differs from group to group. Shaving among women is primarily practiced in the US and Britain, and less so in other countries (although this is changing). And we'll see about hairy fashion sooner or later :)