The thing that I study, poetry, is something that, for me, occupies the highest scale of value. In other words, it is valuable for its own sake, not because it props up something else more valuable than that. So the argument that reading poetry makes you a better citizen if fine. If you want to make that argument, go ahead, I think it is fine, though I might not agree (it would depend on how you frame it and how well you argue it.) But the fallacy here is that we need poetry to serve some other end before we accept is as valid, when actually poetry already occupies the highest tier, since it is a supreme exercise of the human intelligence and imagination. Citizenship is also a fine thing, one that occupies the highest tier as well, but it can do that with or without the support of any particular art form.
Once I realized that, I was able to devote myself more wholeheartedly to what I do. It doesn't matter to me much whether other people share this high estimation of poetry. Many won't. But when I am this enthusiastic then something rubs off on the students.