Approximately every two weeks, I go on a mini-rant on Twitter about people pointing out Republican hypocrisy. The most recent occasion was a juxtaposition between two tweets from Newt Gingrich, one praising the special prosecutor and the other freaking out over him. Clearly, the two tweets were saying different and incompatible things. That is indisputable. The deeper truth here, though, is that someone spent part of their finite time on earth reading, studying, and screen-capping tweets from Newt Gingrich, in the apparent belief that this would produce some kind of political result. I mourn for that person’s lost time, for irreplaceable moments of life that they will never get back.
And why do I mourn? Because Newt Gingrich just kind of “says stuff.” We all know this. He says whatever seems helpful to his personal ambitions and those of the movement with which he is aligned. Often, this takes the form of saying things solely to piss off liberals. He is not making an argument. He is not striving for consistency. He is not even really trying to persuade people of anything, at least not in a sense that would be familiar in a classroom, for instance.
Arguing against self-serving bullshit is worse than a waste of time — it degrades the very idea of debate. It spuriously grants bullshit the dignity of an argument. You can’t debate with Newt Gingrich because he’s not debating. He’s fighting. And though he is a political non-entity right now, he led a nationwide movement that just about strangled the Clinton presidency to death (and arguably made a second Clinton presidency impossible by spreading crazy accusations and conspiracy theories). So at this late date, for people not to know what Newt Gingrich is, for people to approach him as though he’s a potential dialogue partner even in the minimal mode of pointing out that he’s not — it’s upsetting.
This is not to say that politics shouldn’t be about persuasion, but persuasion isn’t about winning the argument. In fact, winning the argument can often make people hate and distrust you. (See, for example, the last forty years of US politics.)
An und für sich 
Oy. You’re not wrong, exactly, and I’m not saying this is an effective tactic. But isn’t there some value in continually making it clear that Gingrich (and the rest of his ilk) do just say stuff, that there’s no point in dialog with him? It’s not about winning an argument with Gingrich himself, it’s publicizing the fact that he’s not worth talking to, for people who haven’t been paying enough attention that they know already.
But you’re right that it doesn’t actually work.
Or we could just put forward our own program and views as convincingly as possible. Just admit that no debate is possible and it’s just competing monologues.