If a person poses a false choice between two options, A and B, then she commits the fallacy of false alternatives, even if she doesn't put forward an argument that includes the false choice.

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The fallacy of false alternatives, also known as a false dilemma or false dichotomy, occurs when someone incorrectly claims that there are only two options or solutions to a problem, ignoring other viable alternatives. This fallacy can be committed even without presenting a formal argument, simply by framing a situation as having only two options when, in fact, more exist.

If a Person Poses a False Choice Between Two Options