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You may have proven that men have an advantage in the average case due to inherent misogyny

I haven't, because those numbers themselves can't prove that.

What they can tell you is that any individual woman playing chess at high levels is vastly outnumbered by men. All things being equal, that also makes women much less likely to win tournament titles (or even qualify for tournaments), if no titles or tournaments do anything to compensate. The result would be that women are likely to become invisible whenever you watch any sort of 'high level' chess – and that can have consequences reinforcing the underlying issue.

The commenter I replied to theorised that the underlying motivation for having 'gender segregated' (which in reality equates to female-exclusive) titles was a fear of women winning. In fact, the opposite seems to be the case. That's what my argument adresses – not the trans issue.