When someone makes an argument by analogy between A and B, and then an opponent replies with an argument by analogy between C and B, which he believes to be more illuminating, the opponent's argument is called a(n):

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The opponent's response is called a counter-analogy because they are countering the original analogy between A and B with a new analogy between C and B. This is a common tactic in argumentation and can be effective in highlighting flaws in the original analogy.

When Someone Makes an Argument by Analogy Between a and B