illustrations illustrate - they do not prove arguments

So often when thinking things out or in a discussion with someone the first person puts forth proof for an argument and the second refutes it with an illustration of his proof. But notice the proof is glaringly missing. All we have is the illustration of it, like a phantom shadow cast on a screen that disappears when the shade is put up. Recently on Imus Dick Cavett gave an entertainingly put illustration to refute the argument that government gun control leads to more controls. It is obvious, forever it seems, a non debatable fact that government rules, like taxes and spending, just keep on eating obese like toward complete control of their goal. Dick Cavett appeared to refute this argument by saying not so, taking one step toward China does not get you to China. So what, one might ask? Well, for openers this should be refuted on the spot as nonsense but is often let go as unanswered proof, even pinning the nonsense on the other, opposing, argument. Therefore this sort of display is not a rational discussion and one is wasting their time listening to it. The best thing, when things this heavy, is to just lighten up.