A good analogy for requiring mixed-sex golf courses would be requiring mixed-sex rest rooms. In both activities, women take longer and require different facilities (e.g., shorter tees).
I have no horse in this race except hoping someone will win a fight with NOW. This may be the one!
Considering the quality of the golf I've seen a lot of guys play, you don't want to got there, pard. There's got to be something else at work here. A wee bit of misogyny perhaps?