I think the "advantage" is strictly numbers based...there are simply more men that play and the larger the sample size the more likely it is to find someone who can play at the higher levels. This has nothing to do with innate ability, and more to do with statistics.
I'm not making any statements about the fundamental differences between men and women...I don't know enough to make such statements. What I do know is that there is some part of the explanation that must be attributed to the difference in the number of total female players vs total male players.
A group of 1,000 randomly selected pool players is likely to have more world beaters than a group of 100 randomly selected pool players, regardless of anything else.
Just something to keep in mind for this type of discussion.
Well first you said that the disparity between the skill of men and women was "strictly numbers based", and had "nothing to do with innate ability". This is a definitive statement about the fundamental differences between men and women, and you are saying there is absolutely no difference. But then you go on to say "I'm not making any statements about the fundamental differences between men and women...I don't know enough to make such statements" even after you just finished making a statement about the fundamental differences between men and women. You totally contradicted yourself. Pick one. Which do you really believe because you obviously can't believe two totally opposite things even though that is exactly what you stated.
Your point about there being more men than women that play and therefore it is more likely that there are better men players is a valid one. Can't dispute that "a group of 1,000 randomly selected pool players is likely to have more world beaters than a group of 100 randomly selected pool players, regardless of anything else." But at various points over time the best player from the group of 100 is going to be better than the best player from the group of 1000 (in this example it would be about a 10% chance that the best player from the two groups came from the group of 100, and over time it would be about 10% of the time that the best current player out of the two groups was coming from the group of 100). And if men outnumbered women 10 to 1 in pool it would also be about 10% of the time that the current best player on earth at that moment was a woman if men and women were truly equal. If men and women were truly biologically equal for pool that point (where the best player on earth at that moment was a woman) would have already happened, and many times. Yet it never has happened, and hasn't even gotten close.
The real question is if you took 100 random males, and 100 random females, and gave them all the same pool instruction and they all practiced the same 8 hours a day for two years, and they all gambled or did not gamble the exact same amount, and everything else absolutely identical, would there be any differences in the abilities between the two groups? If men and women are truly born equal then there would be no differences whatsoever. Out of those 200 players it would be exactly equally likely that the very best player among them would be either male or female. Their ranking by sex would be a random distribution as well, roughly looking something like top player is female, second best is male, third best is female, fourth best is male, fifth best is female, sixth best is male, seventh best is female and so on alternating back and forth all the way down to to the last place 200th best.
But anybody who is being honest with themselves instead of being blinded by their bias knows that is not even remotely close to how it would look. It would look about like what we see in the real world today. The very best woman out of the 200 people would probably be ranked like 15th. The bottom half of the field would be far more women than men. And the only explanation for this is because of our biological differences that we are born with and where men have the advantage, and most likely it is both the physical and and the mental differences that cause the separation but there is some room for debate on what percentage of the male superiority in pool is from the physical and what percentage is from the mental. There isn't really any room for debate on whether there is a biological born advantage though. The evidence for that far surpasses overwhelming and it takes nothing short of massive bias to ignore that evidence. We have to be careful to always see things for the way they really are, even when we don't like it, instead of seeing things the way we wish they were even though it isn't the truth or the reality. Forget about other people...it is being honest with ourselves that is often the hardest by far.