No where did I ever say that there wasn't physical differences, nor did I say that they don't impact athletic ability. There are physical difference with other men as well that effect athletic ability. That's why there are different weight classes in boxing, wrestling, etc. The reason men normally run faster than women is because men have larger hearts. That doesn't mean they can't compete against each other. It also doesn't mean that women would always lose. I was on the Wyoming state swim team when I was younger. There where plenty of girls my age, and my size who could out swim me, who had higher stamina and strength.
The reason there are different leagues isn't because of athletic ability, but because sports have been designed around men. Remember WW2, the outcry and how upsetting it was when the first all women baseball team was created? It is all tied to the same line of thinking, that girls don't belong in sports, and that they aren't capable of doing it. Yet, we see news articles where women are competing in men's sports against men, like football, etc. and doing just as well. Not at the professional level because the majority are still stuck in thinking that men and women can't compete, much like yourselves. It's the same wrong thinking that goes with the "women can't be combat jet pilots" or "women can't be seal team members" etc. Guess what, they are proving that line of thinking wrong. The issue is deeply rooted in our culture, and society, world wide, and that way of thinking, and has nothing to do with athletic ability. Because of the way our culture is, and how many in society view it, I can't give you any active examples of women vs men combat sports because society is still stuck in "woman can't do it" phase, and they don't really exist in the sports world yet. But I can give you real live non sports examples: Women seal team members. Police officers (they are trained to take down bigger and stronger). Do you think they are trained to only go up against women? Get out of here. One sports example I can give you is Motocross racing, not professional, but there are many clubs around the nations that have races that include both genders. it is a very physical sport that requires strength, and stamina. Guess what, women win the races all the time. (I have a niece who competes in such races and beats those so called tougher men). If you go back and read my first post, I said that once it all balances out with transgenders, there would be guidelines and regulations put in place to make if fair and balanced. Just like there are currently in boxing, like weight classes and such.
Find any example, outside of ultra distance running and maybe figure skating, where women and men are equivalent in a sport. Of course, there are women that could beat most men at any given sport. But you can't compare a pro woman against an amateur man and claim parity.
But you are basically claiming the reason women can't hang with men is because they have been trained to be soft by society and don't put in the effort. But I have news for you, the female Olympic runners are putting in a shit ton more effort, with much more sophisticated training than the 17 year-old boy at my local high school that could beat them. Serena Williams puts in a ton of effort and has some of the best coaches in the world, yet a nobody male could (and has) beaten her.
Obviously I am not talking about motor sports. I see no reason why women couldn't compete in motor sports if given equal opportunity. I am talking about human powered sports.
A random example, 2016 100M Butterfly. The woman set a world record, would've been forth from last place against the men*. 400M Dash, the woman would've been second from last against the men*. Marathon, the woman would've finished 92nd.
Of course any of these women would kick the shit out of the vast majority of males, but they are not at parity with equivalent level males, and it is not from a training difference or societal difference. In reality, Olympic sports probably get a higher level of female athlete than male athlete, since many other male sports provide easier paths to college and high earning professional sports.
*The men's time here were qualifying heat times, which are slower than the times during the finals, so it isn't a real apples to apples.
I also don't believe there have ever been any female Navy Seals at the moment. Not that they can't get there, but again it isn't parity there either.
BTW: Accepting reality isn't being sexist. I think women should be given every opportunity to compete and train. And I think male leagues should be open, so if a woman was able to compete with them she should be allowed to. But I also think woman should have female leagues where they can compete against people with the same biological advantages and disadvantages.
Also, if any promoter thought their female boxer could win against a professional male, they'd make it happen. The PPV for it would be massive. The most famous UFC person was a woman for a long time, but they never even put her up a worst ranked male. Of course she could easily beat the shit out of me, though.