I think there are several different motivations.

First, I've seen cats chew up cardboard boxes in order to shape them. This side is in my way, I'm gonna saw it off, and the only saw I have is my face. ergo: cronch.

Second, humans like chewing on things like crunchy potato chips. Imagine if you had long pointy fangs, wouldn't it be satisfying to sink your teeth into something like cardboard?