A false dichotomy is when a speaker implies (or directly states) that there are only two possible options for consideration, and these options are mutually exclusive (only one or the other can occur) and collectively exhaustive (no other options exist).

The argument then follows that if you can disprove even one tiny aspect of argument (A), it follows that argument (B) must therefore be true, as there is no other possibility.

The classic example pits Intelligent Design proponents against evolution. They attack evolution from the standpoint of needing to prove only that there is something wrong with current evolution theory, and then Intelligent Design would become the de facto "winner".

This was evident in the 2005 Kitzmiller v. Dover (Pennsylvania) case in the United States. The US District Judge (John E. Jones III), however, was not fooled:

[Intelligent Design] is at bottom premised upon a false dichotomy, namely, that to the extent evolutionary theory is discredited, ID is confirmed. (5:41 (Pennock)). This argument is not brought to this Court anew, and in fact, the same argument, termed "contrived dualism" in McLean, was employed by creationists in the 1980's to support "creation science." The court in McLean noted the "fallacious pedagogy of the two model approach" and that "[i]n efforts to establish 'evidence' in support of creation science, the defendants relied upon the same false premise as the two model approach . . . all evidence which criticized evolutionary theory was proof in support of creation science." McLean, 529 F. Supp. at 1267, 1269. We do not find this false dichotomy any more availing to justify ID today than it was to justify creation science two decades ago.

False dichotomy is when somebody misreppresents a situation by cliaming there are only two options to choose from, when in reality there may be a whole spectrum of various choices or more sophisticated positions.

Some classic examples might be...

"You're either with us or against us."

"So you say you're not a Christian - well then you admit you worship the devil."