I'll take a bit of a counter to what others are saying. Debating and winning (as distinct from being rational and holding true beliefs) can be fun. Be very clear (with yourself) why you're engaging, and what you hope to accomplish from it, but you don't need to stay away entirely.
First, limit yourself to a few communities that you have at least a little respect for. Most sites you're better off just not looking at the comments, and certainly not responding. Even in good groups, there will be prolific posters you should ignore - just don't respond to them unless someone you do respect chimes in.
Second, don't engage with the portion of their arguments that you think is irrelevant. If the comment is purely about you, rather than your thesis, ignore it. If it's a mix of relevant and irrelvant comments, respond only to the relevant and ignore the rest.
Third, realize that in most cases the readers far outnumber the commenters, and your goal isn't to get another commenter to publicly agree or apologize or anything of the sort. Your goal is to convince the readers (or convince them to respect you enough to comment if you're wrong). Post in a way that is high-status to your intended audience, and let the others seem like the petty idiots they are.
Be very clear (with yourself) why you're engaging...
This is key because sometimes I just want to "win for the glory" and I forget why I started the argument in the first place.
Post in a way that is high-status to your intended audience, and let the others seem like the petty idiots they are.
This is a good strategy rather than focusing on the snotty comments that only irritate.
Especially in the comments of political articles or about economic issues I find myself arguing with people who question my authority about a topic rather than refute my arguments.
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Examples may be:
1:
Me: I think money printing by the Fed will cause inflation if they continue like this.
Random commenter: Are you an economist?
Me: I am not, but it's not relevant.
Random commenter: Ok, so you are clueless.
2:
Me: The current strategy to fight terror is not working because ISIS is growing.
Random commenter: What would you do to stop terrorism?
Me: I have an idea of what I would do, but it's not relevant because I'm not an expert, but do you think the current strategy is working?
Random commenter: So you don't know what you are talking about.
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It is not about my opinions above, or even if I am right or not, I would gladly change my opinion after a debate, but I think that I am being disqualified unfairly.
If I am right, how should I answer or continue these conversations?