Per Yahoo:
Businesses began “encouraging” American women to shave their underarms around 1915, when sleeveless fashions became popular. Harper’s Bazaar featured an ad stating: “Summer Dress and Modern Dancing combine to make necessary the removal of objectionable hair.” Yet another revenue stream made possible by human insecurity.
The war against nature’s leg warmers came a bit later, as changes in clothing allowed women to display more than just an ankle. According to Hope, convincing women to shave their legs was more challenging, so advertisers pulled out all the stops. “Some advertisers as well as an increasing number of fashion and beauty writers harped on the idea that female leg hair was a curse.”
The Straight Dope offers another theory for the surge in leg shaving in the 1940s—Betty Grable. The pin-up’s epic legs may have started a trend. Flaunting one’s gams was suddenly “in.” Since short shorts and woolly limbs don’t mix, it was goodbye to hairy legs and hello to something equally pleasant—razor burn.