ystem).
In summary: Mathematics really is about connections and developing provably correct deductions from available information we have about the world. That's not a rhetorical flourish; the field is really a concrete crystallization of all we know about necessary conclusions. Historically it was synonymous with higher education itself, neither of which were considered appropriate for most people. It's unfortunate that in an attempt to pretend that most people in a modern nation understand it, the logical-reasoning component has been largely wrung out of the system, rendering the whole curriculum as not making very much sense.
A question I always ask U.S. non-STEM people who express frustration with their math education: How did you feel about your high-school geometry class, with its emphasis on proofs and justifications? I find that very frequently people respond with, "Oh, that's the only math class I liked; I really enjoyed it!" And my follow-up is to say (again in the U.S. system): that's the only course in high school that counts as real math from a mathematician's perspective (as a prover of theorems). If you like and feel confident with the work in a geometry class, then that's the best possible sign that you're a real mathematical thinker, even if you didn't get that message previously.
I'll end with an open question, to pivot from the original query: Granted that mathematics is the core subject matter of all education in general -- why is education itself now compulsory in modern advanced nations? Maybe it shouldn't be? That's a perhaps more essential and much harder question (and unfortunately not appropriate for S.E. Math Educators).