It's just a simple test - if all permutations of some situation lead to the same outcome, then the outcome cannot be said to be caused by the situation.
Personally, I am not sure how these linguistic details evolved, but I wouldn't be surprised that the original intention was to place a special emphasis on women. Because the word for a mixed group should have been "invented" first, and then a separate word for women added on top.
But don't quote me on that.
But there is an interesting precedent about dual-words (in the languages that have them), where you use a special form of a word to denote groups of two people. And according to research I've seen those words were added after a word for a group of any size was available - to place a special emphasis on a group of two.