A false dichotomy or false dilemma occurs when an argument presents two options and ignores, either purposefully or out of ignorance, other alternatives.
In general, a false dichotomy gives the impression that the two oppositie options are mutually exclusive (that is, only one of them may be the case, never both) and that at least one of them is true, that is, they represent all of the possible options.
For example, the claim that “you’re either with me, or you’re against me” is an example of a false dichotomy. This form of rhetoric is used to persuade or even threaten, but it ignores the fact that the individual or group addressed may have a neutral opinion towards the speaker. It is logically possible for someone to be neither with nor against an individual.
A more obvious example would be the claim ‘All animals are either mammals or fish.’ We could use that, with the premise ‘my pet parrot is not a mammal’ to conclude that ‘my pet parrot is a fish’. Clearly, something went wrong. The problem here is not a failure of logic in the argument form, but that the first premise is a false dichotomy. That premise is false — there are also birds, for one, as well as other groups of animals.
A special version of this fallacy is known as falsum in uno, falsum in omnibus, essentially “false in something, false in everything”. This is a combination of a false dichotomy and an ad hominem attack, because it attempts to disregard everything the person is saying by the claim that they’re either presenting the truth or presenting falsehoods. It ignores the possibility that the individual is wrong about one thing but right about others. The fact that someone has been proven wrong about claims they made is a potential reason to suspect other claims they make, but not a logical reason to disregard them entirely.