I understand how to construct a proof by induction. I've used it many times, for homework because it was clearly what the book wanted, but when I've tried it in a research setting, it's because I have so little control of the objects in working with. So it has become my impression that since induction is non constructive, when you are able to use it, it's a way of saying: "I don't know why it happens, but it always does." It seems to me like induction is just really convincing. Of course, I'm wrong, I'm just trying to think about why I'm wrong.