I have a friend who once wrote an entire essay (for English) about how he doesn't understand why he, a future engineer, needs to take English or be required to read certain books. I have another friend who's annoyed that important college-entrance things like the ACT require him to do math, even though he wants to go into theatre, which isn't exactly math-intensive.
Personally I'm on the side in favor of English, but I'd argue against both of them--not that I think a theatre major will ever need to use math beyond maybe geometry, but because I basically figure that knowing things is good.
Then again, I'm one of those crazy people who finds most things at least a little bit interesting, so that helps. In Spiderman last night when Harry asks Peter, "Who'd want to know that?" and he replied "Who wouldn't want to know that?" I thought "YOU UNDERSTAND ME!"
I agree that at some point it only makes sense to focus in on one area and not bother learning the other stuff, but I'm not exactly sure when that should be. Because on the one hand, if you really don't care about xyz and really don't think you'll ever want/need to know it, you shouldn't have to waste your time. But I also think that the more you know just in general, the better off you are.
Or, you know, maybe I just feel better about myself when I know things.