If someone is trying to win an argument, the odds of your convincing them are very low regardless of how right you are. The point of arguing would be to make him lose, that is, to convince the audience and not the opponent.

This is a big difference between internet discussions and in person discussions -- in real life the audience is often zero or small, and a person's wrongness will be quickly forgotten, but when someone is wrong on the internet, it is more important.