There is little point trying to shift Math out of their entrenched views but I would just say to parents in UK schools now that, especially for girls, showing an interest in STEM subjects in our state and private schools, primary and secondary, definitely does not lead to any adverse pressure from peers or otherwise (unless of course it exists in the family, of course in many families being interested in any academic subject is met with incomprehension) but the reverse. When my DD dissected a fish instead of drawing it in art in Year 5 it was celebrated in school assembly and my DD has had nothing but encouragement, and her interest and achievement has been celebrated, and the same is true of her peers in local state schools. Science in primary schools is both an important part of the Key stage curriculums and designed to be engaging, and to say that there is not the same emphasis on numeracy as literacy is complete rot. Science and Maths classes in Secondary schools are neither short of pupils or of girls
However in Science classes in mixed schools there does seem to be an issue with the culture that develops within the classes that puts girls off. I suspect this has more to do with adolescent boys flexing their patriarchal wings but now the issue has been highlighted hopefully teachers can address it by varying teaching styles etc. so they have less chance to dominate the discourse. Science is becoming aware that some of it's paradigms, especially in Physics, are also gendered and this is something more fundamental that needs to be studied and addressed. No different to investment banking
Now my DDs research team is up to PhD level equally gendered, and once again the fact that she is a woman definitely marks her out for what might amount not just to positive encouragement but positive discrimination.
As Gently has highlighted opting for humanities is where the adverse pressure comes in. That pressure tends to arise from the perception that a Humanities degree closes down career options. As Jilly highlights that is not true. Not getting strings of As and a 2.1 is what closes down options on graduate entry schemes, and relevant work experience, lots of it, that is the trap that pupils of either sex can fall into if they are not capable of excelling in STEM subjects, however hard they work. The Chemistry A2 regularly trips up even those with the ability and work ethic. In the case of the management entry schemes that many will end up on directly or indirectly employers are interested in a range of skills, experience (those gained in university just a part) and personal qualities relevent to their organisations needs. They full know the they will need to develop their managers further with job specific skills including communication skills /strategic analysis and planning / stats / modelling /computer /finance and accounting skills all of which will be different to anything taught in all but the universities that work very closely with industry.
As far as specialisation goes, sixth form pupils in this area, both state and private, do have a choice. They can opt for IB which means pupils continue with a broader education, it is perceived as more work than 3A levels but within that the work is not as in depth in terms of the knowledge and skills required in the specialist areas, though continued breadth. The IB qualification is one that is more valued globally where specialisation at 16 is not the norm. However many pupils do decide to specialise because they want the greater depth. I agree with summerends these pupils are not idiots and they do have a right to decide what they want to do with their lives in the short and long term provided they get sound advice.
And by far the most concerning issue is that our MFL courses in universities are dominated by private school pupils. Languages are going to be a crucial skill for those wanting to compete in an increasingly global economy, in a changing world, not just in terms of the linguistic skills but the ability to understand the perspective of different cultures. We, and I mean the western English speaking world, really cannot continue shouting loudly and slowly at the rest of the world.
In my friends rural NI school their issue is not whether the pupils opt for STEM subjects though, but whether they can be persuaded (and it is not for want of trying) to do any academic subjects at all, it is the business studies, tourism etc courses that are popular. Without any parental expectations they are the path of most interest / least resistance and then lead to mediocre courses with low grade requirements. That is poverty of ambition though, not gendered.