I've taught many shooting classes with about an equal mix of both men and women, and I would qualify and rephrase your above statement.
It isn't so much that women "outshoot" men, but more a case that an untrained woman can be trained easier than an untrained man. I can teach a woman to shoot in less time and fewer rounds than a man, but it doesn't take that long for the men to catch up with the woman. Beyond the level of a beginner I would say it is pretty much a wash, with men and women having the same average natural ability at punching holes in paper. They just have different learning curves.
I will add that there are tactical shooting scenarios where clear cognitive differences between genders are evident but that has less to do with the simple act of shooting accurately itself.
I stand somewhat corrected. I don't shoot competition, nor do I follow it, because no matter how well I shoot (and I'm pretty good), I will always have the self-esteem problem of thinking that I'm not good enough.
I sincerely believe, because women do "take" to instruction more readily, that if there were more women in the sport of competitve shooting, you would see that women would overtake men in the accuracy category. Because there are far fewer women, the competition, by sheer numbers alone, is not as stiff.
There's a latent talent out there that needs to be tapped. Too bad that the attitudes of some posters here (you are *not* included in this statement) is precisely what prevents women from becoming experienced shooters.