I am not going to go on from here and talk about civility. Clearly, those who use words like "libtard" (or comparable epithets like "Repugnican") do not give any thought to being civil. But many people who talk this way do seem to labor under the illusion that they are being persuasive--that they can "win" arguments simply by humiliating other people and criticizIng them in strong enough terms.
Whether they are right or not depends on what we mean by "winning. If winning an argument means making the emotional cost of offering an opinion so high that people stop participating in the political process, then, unfortunately, it is possible to win by insulting anybody we disagree with. If enough people play this way, we will end up with a public sphere inhabited only by people with thick skins, big mouths, and a penchant for ridiculous hyperbole. In many ways we have already arrived.But there is another way to win an argument. We can actually persuade somebody of something, or at least get somebody to see something a little bit differently than they did before. We can work to change somebody's mind.
This is a much harder thing to do, of course. We can't do it by being sarcastic. We can't do it by getting mad and yelling. We can't even do it by thinking up clever ways to show people how wrong they are. Persuasion is possible; people do change their minds about things--that's why advertising works. But it isn't easy.
Actually persuading somebody of something requires us to create a non-confrontational environment. It requires us to listen to somebody else's point of view, locate areas of agreement, and build on common understanding. And it requires us to risk changing our own minds too. But democracy cannot flourish without these kinds of arguments. They are the foundation of our political process--everybody can try to persuade the rest of us of anything, and whoever gets the most votes wins.
Anyone who genuinely believes that a particular policy or principle is important has a moral responsibility to persuade other people that they are right. We can't do this by yelling at people. We can't do it by calling them names, or sneering, or finding clever ways to say, "I'm right and you're a pig." Nobody has ever been humiliated into a new opinion. Persuasion requires good relationships, civil discussion, and the possibility that we might be persuaded back. But if we cannot learn how to argue in a way that actually persuades people of things, we are not truly taking responsibility for our own beliefs.