For one thing, it assumes that a small alleged "biological difference" is sufficient to explain a gigantic observed effect. If we were to suppose that this difference translated directly into a difference of precisely the same magnitude in programming competence, it still would not be enough to account for the amount of skew observed in actual gender ratios in programming.
The supposedly rational author and his supposedly rational fans apparently are happy to overlook this, however. Running the numbers and figuring out what the expected skew would be seemingly has not crossed their minds.
And a larger problem is that this is not the first time someone has made such an argument. It's been made before, many times, in other fields, and was eventually demonstrated to be false: massive disparity turned out to be more a function of bias in hiring and performance evaluations than anything else. The classic example, once again, is classical music, where the very same "women just are naturally less inclined" and "biological differences mean men are just on average better" arguments used to be trotted out to explain gender disparity. Then the classical-music world started using blind auditions (where evaluators could hear a candidate's performance, but not see the candidate or know the candidate's gender until after completing their evaluation). And suddenly... the gender ratio shifted significantly.
Music was one of the first fields to undergo this shift, but wasn't the last. And yet the author of this manifesto seems blissfully unaware of the precedent from other fields where similar arguments were trotted out. Or, to be as charitable as possible, fails to explain why programming deserves to be a special singular exception to the trend of fields arguing "biological differences" and getting served with proof that it was actually bias all along.
And largest of all is the problem that this alleged biological difference, if it were an explanation, would earn a Nobel prize for anyone who could prove it, because within living memory programming had a very different gender ratio (both for programming jobs, and university computer-science enrollment). So this biological difference would have had to have evolved extremely recently, and spread through the human population with incredible rapidity, including likely being CRISPR'd into women who already were working as programmers or studying CS, in order to un-qualify them for it.
In other words, it falls apart on even the most superficial examination of its claims. There is no "taboo" or "facts nobody's allowed to talk about" or "politically incorrect but everybody knows it's true" here. There's just an incredibly shoddy argument which has been debunked more times than anyone cares to count, and yet somehow is still accepted blindly by people who desperately want a justification for tech's gender ratio that doesn't include "this industry discriminates against women".