@DrewDad,
Interesting. Any specific examples of what happens when a mammal mutates and has another vertebra?
It might well be that the beard is, as you say, a bi-product. But it remains strange that the difference between men and women is so marked in terms of facial hair. You'd have thought whatever primary evolutionary change (which meant beards also had to be kept) that happened to men would also have happened to women.
Although you may be right, thinking about it: Testosterone increases muscle build. Men needed the extra muscle to fulfil their social role. The beard is the bi-product of increased testosterone. Therefore the beard is still switched on in the male and finer in the female. Actually it's probably the other way round. Women's testosterone levels dropped when their roles became less physically demanding and their beard is switched off. You may have cracked it.