I'm sure that we've already covered this and probably ad nauseam at that.
Women are not as cardio vascularly strong as men and obviously the higher up the levels of athletic pursuit you go the more marked the difference.
However women, particularly at the higher levels of Womens Football tend to partially offset this by having superior technique.
You may claim not to be sexist but starting an argument with a statement that the top level of womens football is, as you so poetically put it,' pretty gash' does tend to cast some level of doubt on your claim.
Your opening gambit of "Don't be so stupid" also seems to me somewhat dismissive and I would love you to quote me the published scientific evidence that women have far worse balance than men. Perhaps you could let us all know who carried out this research, who their peer reviewers were and which journal(s) it was published in. If it was a PhD Thesis however just let us know who the candidate was and where the Doctorate was researched and I'll do the rest
Thank You