It's hard to explain why it's good to be able to think about these things, but it's hard to explain why it's valuable to be able to think about math and programming (especially to a math class full of skeptical kids). Essentially, a good liberal arts education transforms your world-view of those subjects the same way a good engineering education does. Just like you shouldn't condemn yourself to reinventing Quicksort when you can be capable of more advanced algorithms, nor should you find yourself reinventing Locke when thinking about politics. It is much better to build on the history of thought instead of being doomed to repeat it (and you'll only repeat it satisfactorily if you're a genius anyway).
OK, there are worthless liberal arts educations. But there are also worthless computer science educations, as anyone who's worked with other programmers has discovered.