Originally Posted by StephenH

Personal observations:
Some of the women I know are okay cycling by themselves, whereas some just don't. So you have a perception of physical safety that influences participation.
Group rides are noted for dropping people, which is worse for newbies, which, combined with the above, makes them less desirable for women than for men.
Some women don't like to navigate. (One lady I know said "I never learned to navigate until I got divorced!") That makes solo riding or getting dropped from groups less desirable.
I have no interest in joining a gym and working out there, but I get the impression that is more popular with women.
Long ago when I was more into photography, I heard the same question there. The basic thought that came up was that men liked cameras and women liked taking pictures. That is, the men tended to be gadget-oriented more so than the women, and I assume that crops up in cycling as well. I don't hear too many women going on and on about Hub A is better than Sprocket B.

AntimonySarah mentioned the RUSA figures above. Those are informative. But for perspective, the average RUSA rider tends to be 50'ish or so, and a disproportionate number of the ones that ride a LOT tend to not have any children. Which is to say, they are not your average typical Americans, either. I am very blessed to be able to ride with a few of those 18%, though!