First of all, we advocate for equal pay for equivalent achievement. Being the (for example) fastest woman in the world is an equivalent achievement to being the fastest man. The fact that the fastest man is much faster than the average woman is as relevant as the fastest formula one car being faster than any rally car. A rally car is a different machine, originally adapted from an ordinary saleroom car, rather than specially designed for racing a circuit. It can carry a passenger. It has a smaller engine and is less aerodynamic. It's less efficient at going around a circuit. Lewis Hamilton driving one of those is not a less capable driver, he is simply in a car which is less well adapted for racing. Women in equestrian events, in which the athletic prowess is that of the horse, compete equally with men. In sport, we judge the skill, resourcefulness and mental fortitude of the athlete as well as the raw physical achievement. This is why we are also interested in disability sport and sub-elite sport.
We prize excellence of course but we compare like with like. So I challenge the disability or 13-year-old comparisons here because women's bodies are not damaged or immature by virtue of being female bodies. We are not Formula 2 or 3 cars, or Formula 1 cars with faults. We are a different type of body and the reason it is less effective at sport is because of the adaptations which allow us to gestate and bear children - the size and shape of our pelvis, for example. We are supposed to be like this, it's not the result of an accident or a medical condition.
Also we aren't men-in-waiting. A 13-year-old boy will experience male puberty, become a man and therefore be able to compete at a much higher level than he can currently. His time will come. Women and girls will never turn into men.
The majority of the sports we play now were designed to show off and hone the skills men are particularly proficient in - based on strength and speed. If sport was all events based on balance and flexibility, perhaps you would be questioning whether it was right for men to have their own categories just because they couldn't compete with women.
You describe it as a “privilege” to have categories which exclude people who might beat us - is that your way of describing fair sport? Fairness is essential to the appeal of sport. As I said above, we compare like with like. Nobody would pay to watch my female cat race and beat Usain Bolt. Except once, maybe, for the novelty appeal. We want to see a battle.
But we do not exclude “people” who might beat us - we exclude men, for the same reason that my cat would be excluded from the men's 100m - there is a clear category division. Clearer than age: children mature at different rates, performance declines at different rates. Clearer than disability, which is a spectrum. Female or male is a clear and immutable distinction. As is cat or human.
Having women's sports, or women's toilets etc is not prioritising women's rights. Men have single sex spaces as well. It's giving us an equal shot.
Regarding handicaps - the male athletic performance advantage is so big because it is an accumulation of many different advantages - strength, greater lean mass, different arrangement of ligaments in the shoulder, more efficient transmission of oxygen to muscles, to name but a few. So how do you calculate how big a head start or disadvantage to give? You can't match men and women for size and strength because a man is stronger than a woman of the same height and weight. You can't match their pelvises. The physiological differences make it too complicated to match the person. So you would have to handicap men using average performance markers from both men and women. Gleaned from ooh, I don't know, women's and men's competitions, perhaps? And if a woman wins the 200m over men who are actually racing 220m, or starting 3 seconds after her, what does that prove? That she is the fastest person in the race? Obviously not. She can only ever be the fastest woman. So what is the point?
Handicapping is an option for some sports but it would be just for the sake of pitting men against women.
I take on board that you are trying to engender discussion but people have already thought about all these things and that is why we have women's categories. The physiological sport advantage men have over women will not change. Therefore women will always need our own categories.