Witches can only exist if people believe in them. So the more you deny them, the more it hurts them.

[He rubs at his face, looking very tired.]

I couldn't quite kill her, though. There's one last riddle left that I couldn't answer. I promised her I'd solve it and kill her for good.

[And he's pretty aware that she could have easily stopped him with the other ones if she wanted to. His theories were absurd and he knows it.]