A false dilemma (also called false dichotomy, the either-or fallacy, fallacy of false choice, black-and-white thinking, or the fallacy of exhaustive hypotheses) is a type of logical fallacy that involves a situation in which only two alternatives are considered, when in fact there is at least one additional option. The options may be a position that is between the two extremes (such as when there are shades of grey) or may be a completely different alternative.
False dilemma can arise intentionally, when fallacy is used in an attempt to force a choice (such as, in some contexts, the assertion that "if you are not with us, you are against us"). But the fallacy can also arise simply by accidental omission of additional options rather than by deliberate deception.
Source: Wikipedia
