This is a question that comes up more frequently than any other here with regard to fashion and dress. The answer is: we can't really be sure. The norm of men's hair being shorter than women's is a remarkably persistent thread throughout history. Even just in the West, when we see fashions for short hair on women or long hair on men, they typically do not break through the principle that men's hair should be shorter than women's. For instance, in the 1950s women's hairstyles were often fairly short - look at any photo of Marilyn Monroe - but men's hair was expected to be very close-cut; and on the flip-side, when men in the 1620s and 1640s fashionably had softly curling hair that was anywhere from chin-length to shoulder-length, women's had to be long enough in back to put up. You can take this convention all the way back to the Egyptians and find art showing men with shorter hair than women.

This is an old, old norm that either arose independently in a number of cultures across Europe and the ancient Near East or predates them. We're unlikely to be able to trace it back to its ultimate origin.