Your argument falls apart when you posit "worse at math" as an essentialist trait caused by genetics, without so much as a link to a single study showing this. Saying "Women are just more social on average" does not prove that it is genetic.
You can probably name at least one woman amazing at math, or one woman amazing at programming. The fact that you can name even one counterexample refutes the proposition that all women are predisposed against mathematical thinking genetically.
For references on the biology, read Simon Baron-Cohen or Louann Brizendine.
Regarding your statistical "argument", obviously the example of Lisa Leslie does not mean the median height of women is greater than or equal to the median height of men. Overlap does not imply equality.
I often wonder why people who can understand fine statistical distinctions in other contexts, and are capable of calculating over/under representations down to three decimal points, lose about 50 IQ points on this topic.
It is similar to the selective and highly asymmetric demands for evidence. I assure you, there are reams of papers on Pubmed concerning the effect of fetal testosterone levels on spatial reasoning. Indeed, there are many more such technical papers than there are well-controlled studies on the disparate impact effects of "competitive job postings".
This hard evidence differential obtains in spite of the fact that researchers must conduct their studies under dark of night, lest they meet the fate of Larry Summers.
The Wikipedia category for Women mathematicians [1] has 125 pages, many of which are to women who were not professional mathematicians.
If in response to the challenge "name at least one woman amazing at math" you don't think of Emmy Noether, then you are not all that interested in maths.
I've studied math. The most recent mathematician I can recall by name (due to a few important theorems) has been doing his great work in the 1930s. Most of the stuff is older. I don't care squat about the gender, but they're likely all male.
Looking at gender ratios in students it's about 50-50 now (ETH Zürich, Switzerland), massively thinning out towards the top (professors are just a few out of 50). It'll take time and untill female mathematicians have an about equal importance in the curriculum students learn, likely a few hundres years. Maths really ages slowly (often because theories get update/extended, but the name sticks).
So being able to name female mathematicians imo doesn't have much relevance to the gender discussion. Luckily society changes faster than math ages ;-)
You can probably name at least one woman amazing at math, or one woman amazing at programming. The fact that you can name even one counterexample refutes the proposition that all women are predisposed against mathematical thinking genetically.