However, gender is not a social construct. This is just not debatable, in my opinion.
Gender is absolutely a social construct. Your entire post more or less conflates gender and sex.
Biological sex is hugely important for determining physiological differences between men and women. The only people who argue against this are fringe crazies and tumblr teens. However, just because the means of the two sexes are different doesn't mean there's an incredible amount of overlap between the two distributions. So while there are differences between the average (cis) man and the average (cis) woman, it's to be expected you're going to find deviations from that when you make comparisons between individual men and individual women.
