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, that it is not sufficient evidence to reject the idea, since there may be other evidence that supports the original claim or argument.
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..