You could look at China, which probably funds women's sports as much or even more than men's sports, since they have a higher potential to get Olympic medals against underfunded women's programs in other countries. The women still put in worse times than their male compatriots for runs/swims, they lift at lower weights in the weightlifting competitions. They also have a larger pool of girls to select from due to the gender ratio in the country, especially the rural areas where many athletes come from.
Why would a gender ratio favoring males give them a larger pool to select from? I'm also curious as to if there are actually any statistics on the way that funding is appropriated for athletics in China; I'll admit that I didn't try very hard but I didn't find any. But in any case, funding is certainly not the only issue facing women in sport, especially in a country where foot-binding wasn't especially uncommon 100 years ago.
Having said that, I could see the hypothetical sex gap in something like swimming being quite large as the physical component (versus the mental component) is quite large so being male confers a more considerable advantage.
The genetic freak argument only comes in to play when you're separating the absolute cream of the crop from the other highly skilled professionals. And seriously, do you think there are plenty of Brittany Griner and Serena Williams just wasting away out there? The gap between women and men in physical sports is far far beyond the gap between say Michael Phelps (a physical freak whose entire body is designed for swimming) and the person who finishes 8th in the 100m butterfly. Your chess analogy is correct when it comes to purely mental exercises (aka Judit Polgar and her sister being trained from Day One to be chess experts) but has very little relevance to the topic at large.
Professional athletes already are the cream of the crop. Hell, the people in the minor leagues are the cream of the crop. The people in the women's leagues are the cream of a much smaller and significantly marginalized crop.
The chess analogy was meant to demonstrate that institutions can affect sports. Chess is purely mental, but nearly all sports have at least some mental component and as the mental component becomes a more significant factor, females should in turn become more prominent in the top levels of the sport. But they don't; women are under-represented in all sports, even the purely mental ones.
As an aside, if you happen to feel that chess isn’t a sport, please don't focus on that part of my post.
You literally just asked him to prove that men are naturally better equipped to hit higher physical talents. This is a known aspect about human biology. This is analogous to demanding for evidence of evolution while blatantly ignoring the well documented evidence since the beginning of modern human biology.
I asked him to prove that the gap in gender that exists in sports today is representative of the effect of sexual dimorphism would have on sports if society weren't oriented around professional male sports.
This is a very different question than the one your limited reading comprehension produced.