The point of arguing
Here's how I look at it. On any question where you hold a strong viewpoint, the potential audience can be divided into three groups. There are those who are already strongly in agreement with your own position, those who have already decided firmly in favor of the opposing position, and those who are undecided or at least don't have very strong feelings either way.
There's no point in preaching to the first group. They already agree with you. At best, if your arguments are especially clever or well-formulated, you may be able to show them some pointers about how they can support the cause more effectively.
Nor will preaching to the second group accomplish anything. A person who has a strong opinion about something very rarely changes in it response to a single session of logical argument or emotional appeal, no matter how skillfully presented. If a person enters the discussion with a deep and long-held conviction that abortion is immoral, or that the Koran is the word of God, or that Communism is the only possible way to build a just society, the odds are practically zero that anything you say will make him abandon this opinion. One can speculate about why such convictions are almost impossible to change, but empirical observation shows that they are.
Which leaves the third group. These are the ones who can be persuaded, because they don't already have firm convictions on whatever question is being discussed. Moreover, they can go either way.
So those people -- the undecided -- are the ones to keep in mind in a debate. On the internet, their presence is rarely detectable because they are unlikely to join in. There's not much point in posting a comment that just says "I'm not sure which of you is right." But they are often reading. I've often read comment threads which featured contention over some question on which I hadn't made up my own mind. I seldom post anything on such threads. It's more interesting to watch and see which side can present the more convincing case. At most, I'll ask an occasional question.
This is why things like tone and logic are so important. A lot of the contention one sees on the internet over controversial issues is aptly termed "flaming" -- personal insults, obscene language, sneering contempt for the opposition, all presented in a manner which suggests the person posting it actually thinks he is being clever and witty. It has the same kind of feel as a person telling ugly racist jokes in the secure privacy of a small in-group of like-minded people, knowing that nobody present will call him to account.
But on the internet, you never know who is "present" in the sense of reading. You never know what potential recruits to your own side are instead being turned off by your obnoxious language.
The same is true of extremist, purist rhetoric that damns to the outer darkness everyone who fails to support the entire agenda of the "enlightened". I've often noted how hard-line liberals trash conservatives in general, and hard-line conservatives trash liberals in general, in this way. It's utterly counterproductive. The moderate person who agrees with 90% of your ideology, but feels you are likely to insult and rail at him because he disagrees with the other 10%, is likely to decide it's best to have nothing to do with you or people like you.
In any debate, always keep the undecided reader uppermost in your thinking! You won't convince the person you are arguing with. That isn't the point. There are others reading who are comparing what you say with what he says. If he starts swearing at you and calling you names -- and on the internet, the odds are fairly good that he will -- don't descend to the same level. He's forgotten the audience and started discrediting his own position. Just leave him to it.