The false dichotomy is a logical fallacy in which only a limited number of options are considered in a situation when, in fact, there may very well be more options left unconsidered. Frequently, the person making the argument might express an assumption that there are only two options to choose from. This fallacy is often present in making false assumptions that if a person does not agree with X, they must necessarily be anti-X, when in reality they may hold some intermediate position or be undecided.
Bowell, T., Kemp, G. (2002) “Rhetorical ploys and fallacies.” Critical thinking a concise guide. (p. 147) London: Routledge.