It wasn't specifically a maths or science degree that I encouraged. They were welcome to look at finance, architecture, any branch of engineering, computer science, accounting, applied maths, mathematical modeling, biomechanics, astronomy, actuarial science, geology, any lab science, neuroscience, economics, statistics, etc., etc. STEM is a very wide field.
I don't believe anyone has enough innate talent in anything, or lack thereof ('the maths ability of a teacup') that would make a certain career path inevitable. That sort of thinking has created the current divide where men go into STEM subjects and careers and women do the 'caring career' thing. Accompanying that divide is the regrettable disparity of income between the two general areas.
As well as telling them I would not pay for degrees in English Lit and its ilk, I encouraged the DDs not to pick a career area on the assumption that their income would provide a second family income, with a partner providing the main income. It is hard to guarantee anything about a career when you set off to university with a general aim in mind, but STEM careers tend to pay well and offer the chance of employment upon graduation. Some more than others of course, and none are completely immune to a deep recession. No career offers a guarantee of personal fulfillment either, but being financially independent, able to pay your bills, travel, buy yourself a home, etc., counts for a lot. I think this is an especially important consideration for women.
My DCs are in a system (US) where graduates receive a very broad education even at university level, so a degree in history for instance would mean they would still have done a few years of science or maths or languages at university level en route to a BA, but by the same token a degree in computer science would involve a few years of university level history/psychology/languages/English Lit, etc. But the non arts/humanities BA would lead to more places (and higher paid places) than the Eng Lit degree would. The US also features universities that can cost $40 to $60K per year (160K to 240K for a degree) and while financial aid has covered a lot of the expense for my family so far, parental and student loans can end up being expensive propositions. A pretty much guaranteed paycheque at the end is a highly desirable outcome of a university degree.
So far, the DCs are 'all rounders'. They are in a system that rewards all rounders when it comes to getting into and graduating from universities. I don't have to encourage them to take maths and the hard sciences in school as this is required, just as it is in Ireland where I went to school. However, in the school my DCs are in, maths and science are pegged together, so if you are in an ordinary level maths class you are also in an ordinary level science class. Working as hard at math as every other subject means more doors are open to you down the line, and in fact it is necessary if you want to see those doors open to work hard across the board. You will not get admitted to highly selective universities if you do not excel in all areas and your chances of a career path job upon graduation increase with the selectivity of the university you attend.
The DCs are all rounders because I made them work at art and maths and English Lit and history and biology/physics, etc., even when they didn't want to and even when they laboured under the misapprehension that they had no innate talent in particular areas. What 'suits' a student might not be immediately apparent to anyone until they give it the best try they are capable of.
Thanks to having a maths teacher three years in a row at age 11, 12, and 13 who sucked, DD3 was baffled by maths and very inclined to think she wasn't cut out for the subject. When she got to high school I made her do summer school two years running to get to the point where she could consider applying to the sort of universities that are now on her list, and lo and behold after putting in the sweat and tears it took, she realised that with work and good teachers she could maths to the point where she is considering engineering or computer science or stats and a few other STEM areas. I also have to push her really hard to make an effort in the verbal contribution element of English Lit classes, which she finds very challenging.
My point here is that she didn't understand that she could excel at maths until she tried, and she certainly wouldn't have known how much she likes it without being pushed to engage with it. Same goes for contributing verbally in English. She has always enjoyed art too, and more importantly, is disciplined, organised and a 'finisher' and did very well in her art classes. If she expressed an interest in keeping up art at third level I would certainly urge her to apply to architecture school, but I would have a lot of qualms about giving my blessing to studying costume design.
DD1 started out studying architecture, which she figured was the ideal way to combine her love of maths and physics with her love of art and also end up with a qualification that would lead to a job that would enable her to pay off her education loans and have a lifelong career that would pay as much as she was prepared to make it pay. The real estate crash occurred in her freshman year of university, causing her to (1) get extremely interested in economics and (2) reexamine her career prospects in architecture. She switched to economics with a minor in fine arts. She secured a career-track job offer before graduation.