I think we need to step back and ask ourselves a simple, but important question:

Why do we use tax payer dollars to educate people? (Public schools, subsidized loans, etc)

There are probably a lot of different answers to this question. Some people can probably tell us the causes that motivated people to start public education in the first place. Some people will provide an answer in terms of human rights. Some will make an appeal to the consequences of NOT funding education.

For me, the answer to that question cannot be separated from the answer to a similar question:

What factors are voters considering when they vote for a school budget?

If voters are aware that music programs will be cut without an increased budget, and they vote against an increased budget, then teaching music is not the purpose of school. At least, not in that area. If on the other hand, they vote to save athletic programs, then school is at least partly about athletics.

The purpose of public school is different to different people, and even individual opinions change over time. I can see that people in this thread hold drastically different opinions on the subject.

Is the purpose of public school to bring fulfillment to students?

Is the purpose of public school to reduce crime and welfare dependency?

Is the purpose of public school to funnel new workers into the economy with precisely the right skill distribution to match the available positions?

Is the purpose of public school to create an educated electorate?

Most people probably want their tax dollars used to fulfill more than one purpose, and they prioritize their lists consciously or otherwise. When money is tight, they may decide that they would rather defund something at the bottom of their list that they previously wanted funded.

Currently, we have an abundance of college educated people who are not putting their degrees to use in the economy. Either they remain unemployed, or they work outside the field in which they obtained a degree. Thus, if you focus on economics, it would make sense to stop subsidizing the study of fields that have the highest concentrations of people not utilizing their degrees in the economy. Also, I'm not sure it makes economic sense to subsidize the education of someone who has little talent in the area they wish to study.