I've read quite a bit about Deadpool, up to the point I know he has cancer, and that he has a healing factor. I don't quite get why one doesn't cancel the other out. I know that in Deadpool's case he had the cancer first, but is that the important part?

Likewise, I assume Wolverine has never and could never contact cancer, due to his healing factor which is much stronger than Deadpools.

Is there a discrepancy here? Should a healing factor cure Wade's cancer? Or is he a special case for some reason? For some reason I can't seem to get my brain round this.