Perhaps the sciences are just harder to pretend to care about. I don’t mean that derisively—it’s just that the arts are very approachable because you don’t need to understand everything in order to appreciate it.

Your second statement is the core issue; pretense has nothing to do with it. The sciences are harder to care about because reaping the rewards of science requires reaching a minimal level of competence.

In art or literature teachers are happy to pass students who never really grasp the basics of how literature is constructed and interpreted. They only demand one thing: that you put enough effort into studying basic critical techniques that you learn to imitate them somewhat. Even that is subordinate to their main hope, which is that you see something in a work of art or literature that inspires a new perspective about something in your life or in the world.

A literature class built around those standards is a valuable and enriching experience, and it can even be valuable and enriching for someone really competent who shares the same classroom with people who aren't.

How could that be accomplished in math or science? If you only require that the students engage with the experience of investigating math or science, and you don't require that they develop competence at applying scientific knowledge, then the students will develop appreciation for the field and perhaps some good will and appreciation for people who are competent, but they won't learn anything useful they can apply in their own lives. They won't learn to read popular science articles intelligently. They won't gain a better understanding of their own health. The only positive outcome is that they might believe that scientists are okay people after all and not scary soulless monsters. (A lot of people in academia would consider that a negative outcome anyway.)

To illustrate the contrast, suppose I believe my spouse is cheating on me, and I think of Richard III and recognize the same feelings of anger and paranoia in Richard III's feelings towards his wife, and I gain a richer perspective on the possibility that my spouse is cheating on me. By mandatory general education standards, academia is willing to grant that I have successfully engaged with literature. It doesn't matter whether I understood Shakespeare's devices correctly or how many layers of meaning I penetrated. It doesn't even matter that I got Richard III and Othello mixed up. What matters is that my range and depth of understandings was enriched by my reading of the play. Most importantly, it doesn't matter whether my beliefs about my spouse's behavior are accurate or not. If I decide to trust my spouse, and four years and two children later I find out that my suspicions were founded all along, and two kids grow up with divorced mistrustful parents, then that is not a failure of my literary education.

In contrast to the literary example, if I read the CDC web site about MRSA and then read a web site that says all so-called infections are actually manifestations of nutritional imbalances, and then I decide it's perfectly appropriate to visit my grandmother in the hospital with an uncovered wound on my arm while she's recovering from surgery, then that's a complete failure of my science education, even though I engaged with writing about infection and enriched my range and depth of understandings about infection. Right answers may not be important to the process of doing science, but they are vital to reaping its rewards.

The difference is that art and literature fill the same role that Bertrand Russell described for philosophy (quote from a recent HN thread):

Philosophy is to be studied, not for the sake of any definite answers to its questions, since no definite answers can, as a rule, be known to be true, but rather for the sake of the questions themselves; because these questions enlarge our conception of what is possible, enrich our intellectual imagination and diminish the dogmatic assurance which closes the mind against speculation....

This is the pragmatic approach to literature that colleges would like all graduates to appreciate. That means introductory literature classes can be enriching without demanding that everyone achieve any basic competence at literary analysis. Introductory science courses are useless unless the students achieve some basic level of competence. That means that mandatory science education is a very different proposition from mandatory art and literature courses. The minimum useful standard is much, much higher (unless the purpose of science education is merely to teach people to trust mainstream authorities.)