Many previous writeups hypothesize that the reason shaving is common among U.S. women is to emulate the look of prepubescent boys. I think there's a vastly simpler explanation -- it is a practice designed to exaggerate the differences between male and female secondary sexual characteristics.
Women (in general) have less prominent body hair than men. To look even more "feminine", women may exaggerate this characteristic by shaving, just as they may exaggerate other characteristics that differentiate them from men by wearing push-up bras.
Men are probably not trying to look like goats when they grow beards on their faces, neither are women likely trying to look like prepubescent boys when they shave their legs. The visual similarities are likely coincidental.