womanformallyknownaswoman
Those arguments don't wholly stack up for me, for a variety of reasons.
One interpretation of the recent much publicised study showing gender equality correlates inversely with STEM participation is that, essentially, life quality pressures in poorer / less equal societies push women to engage more with STEM subjects because the payoff is large. There is at least a plausible argument that declining female computer science participation in the west, for example, coincides with an opening up of opportunities in many other fields, including professions (such as law and medicine) which offer greater returns. For there to be an increase in female uptake of CS, there would have to be a decline in women taking different high-status - it's the same population of people.
"Additionally the way to gain IT now is taught by mostly men for men plus the content and delivery in schools and Unis etc doesn't involve enough women"
Computer science is computer science. There is not a gendered interpretation of it. I find the argument that it needs to be 'feminised' to appeal to women somewhat pernicious. Male domination of a field didn't stop women piling into Law and Medicine in huge numbers when those doors opened, to the point that there are now more female than male doctors in the UK (and far more female medical students).
I agree entirely on your points about the remaining barriers to reaching the pinnacles of said professions.
"They make inferences that can't be proved"
I wouldn't make any claim stronger than this - the idea that differences in occupational choice are entirely down to patriarchy, or societal bias, is bunk.
I think the available evidence leans towards there being some genuine, biologically based gender differences in occupation choice. It certainly won't be the whole effect, however.