Biologically, there are differences in many sports, absolutely agree. I don't think pool is one where that is really an issue. I have spoken to a lot of players I respect, many of them professional, who do describe it as 'moving a stick backwards and forwards' - and fervently stating that the defining characteristic of a champion is mental fortitude and strength (psychological strength) - So to me, it becomes especially pertinent that a lot of these biological differences are reinforced and bolstered by societally constructed gender norms, removing opportunity for growth and development in those areas of difference. Psychologically, that socially constructed divide creates a set of fixed expectations of skill that doesn't actually exist.
I too just want an environment where everyone can play their best game. Again, thanks for sharing you viewpoint in a thoughtful and articulate way. I don't have the answers, but I don't think dividing, separating and labelling offers opportunity for everyone to play their best game, to grow and ultimately grow the game we love to play.
Hope you continue to enjoy the game, get better and most importantly, have fun