Why do they have a womans championship? Is there something in chess that skews male?

Chess is unisex and then there's women chess. Women can partecipate in open tournaments.

So women can compete in mens but not vice versa? Do men have an advantage?

Women have a lower winrate in open tournaments.

Wonder why, no psychical advantage or anything

That's a question that has been asked, and studied, for decades and so far there's no clear answer. There's a lot that suggests that stereotype threat might be a factor (simply being aware of a stereotype makes it more likely to conform to that stereotype).

https://qph.cf2.quoracdn.net/main-qimg-929b67e5b164c180d10d9ece5773f03f

The clear answer

Where's the source and actual study?

https://www.researchgate.net/figure/Gaussian-distribution-of-IQ-of-men-s-162-and-women-s-132_fig1_344751288

There's no correlation between chess ability and IQ...

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