"Two separete sides of the same thing" "cannot happen?" Umm.. I would show him a coin, and point out that it has two seperate, similiar but unique sides, and it yet exists in complete defiance of his logic.
The fact that they're similar only makes them MORE likely to happen, not less. You're right, if that is what he said it's a load of bunk.
Maybe he's trying to argue that fighters don't become casters, but that's kinda what multiclass is all about.
Then I guess you could explain to him that Succubi Paladins are technically legal in D&D even though they have an Evil Subtype and watch his head spin.