"surely a debate/discussion/argument/whatever is all about seeing how strong the other person's case is" - surely it's more about demonstrating that your own case is actually valid, not just stronger than someone you happen to be arguing with.

If you are arguing that the moon is made of green cheese, and I am arguing that it is made of yellow cheese, I might win the argument, since it does looks a lot more yellow than it does green. But that doesn't mean I'm in any way right about the moon.