I do often see people asking why they've been downvoted (and seem genuinely confused), but I don't think it's the right move to require at least one explanation reply.
I'm reminded of the xdcd "someone is wrong on the internet!" comment. I'm starting to get to the point where I don't feel like arguing or even explaining things; I just want to downvote, move on, and hope my moderation contribution has made the shape of the thread more useful to people.
If I had to explain my downvotes every time, I'd hardly ever bother, and I suspect that's true for most people. A forum where no one wants to take the time to moderate is not going to be a healthy place.