The point of the analogy wasn't to say those two things are the same. It was reductio ad absurdum, a totally valid proof technique in math and logic.

If person A says "X implies Y", then person B points out that X would also imply obvious nonsense Z, it doesn't mean that B is saying Y and Z are the same, or even that Y isn't true. They're just pointing out that X is too general to possibly be true.