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Will_Sawin comments on Better Disagreement - Less Wrong
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There's a valuable difference between two different kinds of counterarguments (that I encountered in Drescher's Good and Real, but I presume it's widely known):
To correct someone, it is not sufficient to offer an argument for the opposite conclusion. At that point you merely have an apparent paradox - two arguments for opposite conclusions. You must also point out where in their argument they went wrong.
If everyone followed this policy, it could break certain circular or repetitious disputes which are trapped in a cycle of: A offers argument for X, B offers argument for not-X, A repeats their argument more clearly or more loudly, B repeats their argument in turn, and so on.
Doing this is often surprisingly difficult. There's something about analytical frameworks, where to me, A feels like a flaw in the argument to B, whereas to you, B feels like a flaw in the argument to A.
I think one reason for this is that decisions are made in terms of cost-benefit analysis, which tends to make that distinction fuzzier.