This doesn't work as out of a man and woman of the same weight the man will still be stronger on average. Women have a higher body fat percentage, and less muscle in their upper body simply because they have less testosterone. You would probably have to use testosterone as a way of categorizing people in sport. It sucks but there is no other fair way I can see.
There is no "fair". You can't have it. Tall people usually win in basketball. Narrow builds do better in marathons. People older for their age bracket (as kids) are more likely to enter the NHL (growing up they're bigger so they get more playing time). So yeah, whatever you do, most of us are starting with a big disadvantage at any sport, even if we put in the same effort our whole lives.
That's life. The question is how to make rules knowing all of that.
Wow, it's almost like trying to measure and codify man- and womanhood is inherently dangerous and phobic, even to cisgendered people who don't meet the nebulous standards set by bigots who are obsessed with other people's genitals, and we should maybe just stop doing that and let people identify themselves however they want?
Babyslime is the woman who decided to have no prenatal care at all for her second pregnancy, and delivered a baby with mermaid syndrome (sirenomelia) which is linked to uncontrolled maternal gestational diabetes, and when the baby was breech and she was in labour at like 28 weeks, the obstetrician told her he had to do a C section, and she spent the rest of her time on her blog claiming she was medically raped or birth raped. She is a shitty person.
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It's really simple. If you're born with a vagina and you naturally have elevated testosterone levels, you're a man. If you have a vagina and you take testosterone, you're a woman. But also if you have a vagina, you'll never be a man. But also if you have higher testosterone then you were never a woman. Woman never yes man a vagina testosterone no was an elevated. Vagina man.