Man, I feel lucky - I was required to take shop - small engines, plastics (vacuum forming, polystyrene bead molding) and woodshop in middle school, along with every other student, male and female both. Also required were Home Economics classes - cooking and sewing. I liked the shop stuff but was already tinkering around on my own at home; I was also cooking (part of growing up in our family) and had been taught to use a sewing machine - I think the use of the "thread injector" is a great skill - think Tactical Tailor. I'd love to have an industrial machine at home - I'd be prototyping all kinds of packs and bags, tactical kilts and the like. I would like to learn welding - which I still can, if I could find the time; there's a maker space within walking distance (like, .2 miles close) of my house that has classes in that stuff regularly.
I guess I generally learn by doing - though only with hands on kinds of skills. Higher order math - that's what school was for. Actually, the math turns out to be a pretty vital skill, IMO; I feel like it taught me general problem solving and troubleshooting as a byproduct. And since I have children, it comes in handy there as well - someone has to help them with their homework.
If you've got the cojones and your head is attached firmly, learning to arc weld would only require some $$ and a commitment to failure. If you can buy a welder at HD, it probably isn't impossible to learn.
