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?
You simply need to debate in places that have a certain highbrow barrier to entry. For example, places where people self-identify as economists, such as comments in Marginal Revolution, because they want to signal not only blue or red tribe membership, but also the economist tribe membership. And that makes them want to focus on arguments of the better kind.