I have the following set of regulations for internet arguments, taken from the philosopher Mortimer Adler:
Before you can disagree with someone, you must
completely understand.
Without understanding, both of you are not talking about the same thing. I find this common in religious debates, where an atheist is attacking Christian beliefs, faced against a non-Christian theist. So someone might argue that God can't possibly be omnipotent, but their opponent might be Norse and doesn't even believe that his gods are omnipotent. The two end up beating up straw men.
When you disagree, do so with the purpose of learning more or correcting someone. Never do it to prove someone wrong. A guideline is that
you should feel no pain in agreeing with the person.
If it hurts you to admit that the person is right, then walk away. The argument ends up personal.
All disagreements need a reason.
If you're going to disagree, it must meet one of the following criteria:
1. Show that the other person is uninformed - that they're lacking knowledge that you have. If someone writes a formula involving division by zero, you can point out that they can't divide by zero. But you shouldn't make an appeal to expertise and tell them that they can't use formulas until they have a PhD in mathematics.
2. Show that the other person is misinformed - that they made a false assumption somewhere. Don't assume that the act of assuming is bad, but rather prove that a specific assumption is false. Prove that the logic is
not sound.
3. Show where the analysis is incomplete. A lot of old books, like Sun Tzu's Art of War is correct, but incomplete. For example, Sun Tzu talks about 'death ground' strengthening the resolve of soldiers, but the entrapment/'scorpion' strategy used by generals like Hannibal and Khalid made use of putting people on 'death ground' to panic. Sun Tzu was not wrong, but he did not bring up situations where death ground was a bad thing.
If you can't do one of these three, then you can't really disagree. You can say that you don't like the conclusion of the argument, but you can't quite say they were wrong.