Here is a fun visualization of the types of disagreement you may find on the Internet, as described by a fellow named Paul Graham. You should click that link and read the whole thing on his website, but in any case here is the intro and the hierarchy.
The web is turning writing into a conversation. Twenty years ago, writers wrote and readers read. The web lets readers respond, and increasingly they do—in comment threads, on forums, and in their own blog posts.
Many who respond to something disagree with it. That’s to be expected. Agreeing tends to motivate people less than disagreeing. And when you agree there’s less to say. You could expand on something the author said, but he has probably already explored the most interesting implications. When you disagree you’re entering territory he may not have explored.
The result is there’s a lot more disagreeing going on, especially measured by the word. That doesn’t mean people are getting angrier. The structural change in the way we communicate is enough to account for it. But though it’s not anger that’s driving the increase in disagreement, there’s a danger that the increase in disagreement will make people angrier. Particularly online, where it’s easy to say things you’d never say face to face.
If we’re all going to be disagreeing more, we should be careful to do it well. What does it mean to disagree well? Most readers can tell the difference between mere name-calling and a carefully reasoned refutation, but I think it would help to put names on the intermediate stages. So here’s an attempt at a disagreement hierarchy: