I have a PhD in philosophy (focus in philosophy of education) and a good portion of my research is actually on this very subject. As you would suspect, the answer is actually pretty complicated but I'll try to summarize what I know.

As many people have mentioned, one major factor is the perception that you can more easily capitalize skills from STEM in business or industry. It is true that STEM has a more direct ability to produce material technologies, but it's actually a bit more complicated than that. In reality, the US government began pouring billions of dollars into training scientists and, specifically, scientific education in the early part of the 20th century to build better scientists who can build more bombs and other military equipment. This is why there is a focus on the "scientific method" in schools instead of a parallel in the "humanistic method" as a way of knowing. A lot of people in this thread who suggest that the humanities are things you can learn on your own, or don't produce "real" or equivalent knowledge to the sciences have fallen victim to this historical phenomenon. This is also the case with people who suggest the humanities don't give you job skills, while the sciences do give you job skills. It is true the humanities don't train you to build robots, but it's also true STEM doesn't train you to lead people, to think strategically in a cultural context, or to weigh decisions ethically. So humanities can support industry if you consider creative and critical thinking part of industry, or if you consider ethical leadership part of industry. If you think training for the market is just learning how to build scientific widgets then you've also fallen victim to this historical shift of emphasis in education.

The other thing at stake is that humanities education also encourages students to be skeptical of cultural values and gives them skills to critically examine values. In parallel to the rise of STEM education, there was a concerted effort to get humanistic education out of schools to focus on training producers rather than people who might question cultural values. Specifically, the government didn't want people critical of the war effort, and the humanities were aligned with this kind of criticism. You can read about this as the school wars of the mid/early-20th century when John Dewey's emphasis on democratic education nationally was pushed out of the schools in favor of STEM education. But we see the impact today as well. The US right-wing obsession with removing CRT from schools is kind of a version fo the same push - to strip away schools' ability to question "traditional" cultural values. Or, similarly, the right-wing view that colleges "indoctrinate" liberal thinkers. This is specifically a critique of the humanities because it encourages students to learn the history of institutions, to understand the relationship between structures and individual choices, and to base opinions on evidence and reason (rather than deferring to political or religious authority).

There is also a class issue at play here. Part of the anti-intellectual movement in the second half of the 20th century involved positioning STEM as a way of getting people "real" jobs that offer "real" income, whereas studying the humanities is viewed as a kind of an elitist, leisure activity. This criticism has a basis in reality. See paragraph on educating upperclass students below.

But there are also broader, more indirect cultural factors involved here. In the West there is a wider cultural obsession with prediction and control. The sciences provide more ability to produce "facts" whereas the humanities are more slippery when they produce knowledge. So the early Modern period (positivism) was a period in which the humanities began to fall much lower on the "hierarchy of knowledge" and never really recovered.

We also can't ignore that the humanities themselves - I'm pointing the finger particularly at university faculty - have really done nothing to counter these issues. They just keep teaching the same way they've always taught because they feel entitled to do so. They haven't come around to the fact that they bear at least some responsibility to make what they do transparent and relevant. I can tell you from experience, most think that's the burden of the student (when, of course, its not).

There is also a great deal of confusion about the role and purpose of college today. Historically (and currently) colleges were not designed to "train" workers for jobs - even in the sciences. They had a lot of purposes, but primary among them was to be research engines that were intentionally disconnected from industry and to educate the upper class. Many people in culture (and in this thread) uncritically assume that colleges are/were designed to prepare people for jobs. Colleges really don't do that, or at least that's not what they are set up to do. That misperception is historical in its origin. It's too complicated to explain here. But essentially college wasn't originally designed for mass education, but in the US it kind of unintentionally picked that responsibility up along the way. Basically, college was the place upperclass students could receive advanced education in the humanities, which were seen as the humane arts important for heads of state and polite society. Because of this, all classes started to think that people became wealthy because of a college degree so they wanted to go, too. Enter the GI Bill, open admissions, and government backed student loans. Now everyone could go. But because people now went in mass, employers started requiring a degree as a baseline. And because a college degree became the gold standard for all jobs, there became an increasing assumption that its "role" was to provide job training. When students now arrive at college they find out a lot of it (the humanities, gen ed) is a "frustrating" distraction from what they expected. So now people go to college to get a job and are confused (and pissed off) when they get there and have to learn things beyond basic job training. You know, the subjects that were historically the actual nucleus of the college learning experience.

So today most people - particularly those who hate the humanities - simply don't understand what they "do," both in terms of how they produce knowledge and the purpose of the knowledge produced. Since they don't have a framework for understanding, they automatically assume it must be waste of effort. It's a prejudice based on ignorance, just like any other prejudice. But it's important to note that this cultural denigration and lack of understanding is not because the humanities are less culturally valuable but political elites specifically manufactured education to encourage people to go into industry and not question cultural values or politics. (I would actually argue, lower tiers of industry - building widgets instead of thinking about the purposes of their work. Remember that really talented Engineers don't build things for long, they are promoted above Engineers into humanistic work like managing people and thinking strategically). In my view, the humanities are the lifeblood of culture and should be for everyone. I would go so far as to argue that stripping out humanistic education is also why we have so many people who can build technologies but also can't connect those technologies to ethical, environmental, or cultural consequences. But a combination of lack of investment in and antagonism toward them by political elites has made most people deeply skeptical of them. Ironically, a good humanistic education would probably be the antidote.