I'll make some observations from a Western perspective (which may or may resonate with a Chinese student, say). Consider: Mathematics has been at the forefront of all education forever -- since long before the idea of compulsory education itself was conceived.
In Classical Athens (~420 BC):
More focused fields of study included mathematics, astronomy,
harmonics and dialectic – all with an emphasis on the development of
philosophical insight. It was seen as necessary for individuals to use
knowledge within a framework of logic and reason... Wealth played an
integral role in classical Athenian Higher Education. In fact, the
amount of Higher Education an individual received often depended on
the ability and the family's willingness to pay for such an
education... Women and slaves were also barred from receiving an
education... The people in a pythagorean society were known as
mathematikoi (μαθηματικοί, Greek for "learners").
A system for higher education was described by Plato, and used as the structure for university studies through medieval and Renaissance Europe:
The quadrivium consisted of arithmetic, geometry, music, and
astronomy. These followed the preparatory work of the trivium,
consisting of grammar, logic, and rhetoric. In turn, the quadrivium
was considered the foundation for the study of philosophy (sometimes
called the "liberal art par excellence") and theology. The quadrivium
was the upper division of the medieval education in the liberal arts,
which comprised arithmetic (number), geometry (number in space), music
(number in time), and astronomy (number in space and time).
Educationally, the trivium and the quadrivium imparted to the student
the seven liberal arts (essential thinking skills) of classical
antiquity.
Note that in each of these systems, mathematics comes first. In the quadrivium, all of the components are actually numerical; including music, which one might consider today as a humanities subject. I'll emphasize again of this all-numerical higher education course: "the quadrivium was considered the foundation for the study of philosophy (sometimes called the 'liberal art par excellence') and theology".
Now, why do these connections and foundations seem hard to understand today? I might suggest that there's been a historical progression in which education and mathematics have become so monumentally important -- an existential issue for any modern nation (say, since the military conflicts in the 19th and 20th centuries) -- that every nation is nearly frantic to produce a maximal number of STEM professionals, scientists, and engineers. These nations have demanded that everyone have some amount of compulsory schooling, with emphasis on the mathematics that would be a pipeline towards engineering and the like (specifically: algebra leading to calculus). Unfortunately, this systemic stress has cracked the educational institutions into producing a Kabuki theater version of mathematics -- students can pass relatively mindless algorithmic tests, without understanding or insightful explanations.
On that latter progression, see Campbell's Law (thinking here in terms of the assessment, "it would be good if students in our schools could get high test scores in math"):
The more any quantitative social indicator is used for social
decision-making, the more subject it will be to corruption pressures
and the more apt it will be to distort and corrupt the social
processes it is intended to monitor.
Perhaps the major missing component, which has set mathematics education on a foundation of sand, is the lack of prior training in logic (see above: in the classic trivium, grammar-logic-rhetoric were prerequisites to the all-mathematics higher education). Without this, mathematics teaching tends to have the appearance of a huge list of random and disconnected non-meaningful procedures, instead of the training in reasoning and persuasive speaking which mathematics was long held out to be (and which you'll hear many mathematics educators proclaim, although it's not generally understandable by recipients of the current educational system).
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).
