Argument from fallacy

The argument from fallacy, also known as the argument to logic (argumentum ad logicam), fallacy fallacy, or fallacist’s fallacy, is dismissing a proposition because one of its supporting arguments contains a logical fallacy.

In other words, the rejection of an idea as false simply because the argument used to support the idea is itself fallacious. Just because one argument lacks merit or is fallacious, it is not sufficient evidence by itself to reject the idea, since there may be other non-fallacious evidence that supports the original claim or argument.

Example of an argument from fallacy

Tom: OK — I’ll prove I’m English — I speak English so that proves it.
Bill: But Americans and Canadians, among others, speak English too. You are assuming that speaking English and being English always go together. That means you are not English..