Actually, your examples prove my point. As children, girls and boys are not substantially different in ability, so obviously they can play together. Competition shooting and motor sports are not dependent on strength, size, speed, agility, etc. In horse racing, women compete with men, but because they are smaller, and they can compete with small, light men.

But you think men should be able to compete in women's soccer, basketball, baseball, hurdles, shot put, hockey?

"You segregate by demonstrated ability, rather than gender." I don't know where you get that from. We never match competitors by equal ability. That would be silly.