False Dichotomy
logical fallacy

Also known as False Dilemma, Bogus Dilemma, Bifurcation, Black-and-White Fallacy, Either-Or Fallacy

A dichotomy is evaluated on a premise that only two alternatives are possible.  This is false when other alternatives are in fact possible, which usually is the case. The notion that a binary choice exists usually is implied rather than being stated explicitly.

Predicate 1:
 Propositions A and B are mutually exclusive
Predicate 2:
 A is {true / false}
Therefore:
 B is inverse of A

Examples:
"You are either with us or against us."  -- George W. Bush, November 6, 2001
If taken literally, this neglects neutrality and mixed allegiance for different elements of a set.  When taken as a rhetorical device, this quote has also been attributed by another source to a fallacy which it identifies as Appeal to Gallery, which corresponds to the fallacies listed here as Appeal to Emotion and Appeal to Fear.