Don't forget, being bigger can be a disadvantage in certain sports.
It can, but in almost every single sport men end up, on average, more capable. I can think of no individual sports where women are superior than men and no team sports where the women's teams are superior to the men's teams. I am sure there's the possibility of one or two exceptions but that would be about it.
Taking the example of football: Personally I am a huge advocate of women's football. It's a great game with healthy role models for young women and girls. It's good to watch. However it is, fundamentally, a different game to the men's game and the two shouldn't normally be compared if you want to appreciate it (I'm about to compare them now!).
I watch a fair bit of women's football. There are a number of differences, some cultural, some due to the fact the game is in its infancy compared to the men's game, and some biological. Remember the game is played on the same size pitch as the men's game, with the same size goals.
Biological:
The game is much slower overall. Players run slower and react slower.
Players have less endurance.
Goalkeepers are smaller. In fact all the players are smaller on average.
The ball cannot be kicked as hard or as far.
Players generally have breasts which raises the centre of gravity of your average player, which affects the speed and effectiveness of players turning under pressure.
Players are weaker.
Players may become pregnant, leading to extended absences and potentially reduced performance upon their return.
The menstrual cycle may affect the performance of some players.
Instinctive decision-making is often poor.
Cultural:
The game is more tolerant of physical contact.
Players exhibit a lower level of severe dissent towards the referee.
Players are more receptive to coaching and the application of tactics.
Women generally start learning the game, and playing seriously, later than men.
There are far more unforced errors caused by a lack of concentration than poor skills.
"Infancy of the game":
There are not enough qualified and experienced women coaches/managers yet.
The quality of some coaching is poor, defending is usually disorganised and the standard of goalkeeping is particularly weak.
Technical skills are usually well-applied and some women players have excellent first touch, close control, and ability to play incisive passes.
Just a brief overview and all my own opinion.
Men indisputably have a significant advantage over women in any given scenario. I am a male footballer and the advantages I have are not because I "identify as a man", they're because I am actually, a man, with all the biological attributes that brings. The World Cup holders in the women's game are the USA, and I have every confidence, everything else being equal, that a non-league men's team would comfortably beat them in a match.
People who were born as male but identify as female should not under any circumstances play in the women's game. It's not fair.
