I think there's just a really big difference between arguing and being assertive. I don't argue - online or off. I have had about five arguments in my life (I remember them all because they are rare!) I can also be unassertive, but generally I am able to speak up.

It's all in how you say it. Now, I probably veer too much the opposite way as I can't express emotion if I'm getting worked up. It's a safety mechanism, I will hide it at all costs, so I have a kind of 'flight to the logical', where I will explain rationally why I disagree with the other person without admitting I am upset. Sometimes it is necessary to at least say that you are upset, even if you don't show it, because people don't understand what kinds of things upset me seeing as I never tell them.

But all in all, just stay away from the personal. If you don't agree with something impersonal - such as a political view - speak your mind but never attack. It's nothing to do with you, after all, and everybody has a right to their own beliefs. You should share your beliefs just as everyone should, but it's fine to disagree. And no one likes someone trying to persuade them out of their political beliefs. We are all allowed to believe what ever we want and we are all allowed to disagree.

If it's about something personal - if someone makes a statement about YOU that you disagree with - then it is very important to say you disagree, but don't do this by attacking back. You'll just end up in a ping pong game. Instead, state your own opinion as a matter of fact. You don't have to persuade them - who cares what they think? - you just have to have your own back.

So, as an example:
"You're upset too often"
"I often feel upset. It's not very nice for me so I'm looking into ways to feel happier. But I disagree there is such a thing as too often. I am allowed to feel whatever I feel."
"No one else is upset as much as you are"
"I doubt that's true, but you're entitled to your opinion"

>If this conversation actually happened this is the point you walk away and choose not to associate with this person, by the way...