At least in our English class, we were taught that the only acceptable response to being asked "How do you do" is to repeat "How do you do" back.

This is actually true, at least in terms of what's 'proper' to say!

However, very few people know about it anymore, at least in the United States-- that's what I was alluding to when I said that "most people of my generation don't really know how to react to this." In fact, I've legitimately never heard anyone other than myself make the "correct" response there.