Not quite sure why you say men are better than women at sport? OK, the physical games to one side, I would suspect that the reason men and women don't compete together in golf is one of tradition; after all, there are still golf clubs which won't even accept female members!
As for table tennis? Don't know. At a local league level, it can be mixed as I remember my father's chagrin when he was thoroughly thrashed by a 16-year-old girl!
Equestrian sports are totally mixed sex and it's probably evens whether a man or a women is champion dressage, show-jumper etc.
Sport is very traditionally based and culturally based. How about .... why aren't there many (if any) black champion swimmers yet they excel at track events?
Cheers
Whirls