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I'm looking for the name of a logical fallacy in which person #1 makes a statement, and person #2 misinterprets it as a far more extreme statement, then rejects the extreme version.

Example (simple but contrived): I say that I've never visited the Grand Canyon. My opponent accuses of me of saying the Grand Canyon doesn't exist, and "proves me wrong" by showing me photographs.

Example (more realistic): I say that people with light skin and dark skin have no significant differences in brain structure, on average. My opponent accuses me of saying that "race is entirely irrelevant" and argues against this more extreme position.

I looked through Wikipedia's list of logical fallacies, and the closest I found is the straw man argument, in which the opponent argues against something the original speaker didn't say. But in my case, the opponent's argument isn't some random & irrelevant topic, but an extreme generalization of the original statement. I'm hoping there is a name for that particular illogical leap.

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It is a "straw man" fallacy, since you never actually said for example that the Grand Canyon doesn't exist. So "straw man" is not wrong, the question is whether there is a more precise case for the circumstances, where the false argument is actually a misrepresentation of something you actually said.

There is "Contextomy" which is basically misquoting what you said. If you said "race is entirely irrelevant to the brain structure", and this was changed to "race is entirely irrelevant", that would be "contextomy". You actually used all the four quoted words and in that order, but something essential was left out.

In practice, you should never, ever let anyone get away with this. Your examples are not mistakes, but intentional mispresentations of what you said. So "I didn't say that" or "I didn't mean it that way" should not be your reply. Your reply should be "You are intentionally mispresenting what I said, you are a liar. "

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