In Canada today women make up over 60 per cent of medical school students and 55 per cent of law school students. This social pressure you're talking about doesn't seem to be working. And frankly, it's hard to believe the public education system could carry out such a program, with over 70 per cent of teachers in primary and secondary education being women. 
Women are outstripping men at every level of education and in every field except STEM. And yet all of the handwringing and outrage about disparity is over STEM. 
Oh, and how do you explain the tremendous over-representation of Asians in the STEM field? Systemic bias? I thought Canadian institutions were racist?