Women do have their own spaces, at least here in the Midwest US. But women tend to think the men are having more fun over in their male-only spaces, so they want into them, and then those spaces become co-ed, and pretty soon the men are looking around for a new male-only space. Not because they don't enjoy spending time with women, but because there's something about a male-only space that lets a man relax and recharge in a different way.

That cycle tends to repeat, and you don't really see it in reverse. Men are mildly curious, at most, about what women do in their own spaces, and generally don't seek to join them. That probably adds to the perception women have that the male-only spaces are more fun.