False dichotomy

Cunningham & Cunningham, Inc

A dichotomy is a set of two mutually exclusive, jointly exhaustive alternatives. Dichotomies are typically expressed with the words "either" and "or", like this: "Either the test is wrong or the program is wrong."

A false dichotomy is a dichotomy that is not jointly exhaustive (there are other alternatives), or that is not mutually exclusive (the alternatives overlap), or that is possibly neither. Note that the example given above is not mutually exclusive, since the test and the program could both be wrong. It's not jointly exhaustive either, since they could both be correct, but it could be a hardware error, a compiler error and so on.

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I think there is another name for the argument where somebody makes a list and tries to say that your answer "has to be on the list." I think the name of that fallacy would have nothing to do with the length of the list. A FalseDichotomy is an attempt to force a person into choosing one of two seeming opposite extremes, not just one of two arbitrary answers. That is why "If you're not with us, you're against us" is a FalseDichotomy -- because the two alternatives are presented as opposite extremes. But "He lives in either New York or Boston" is not.

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Rational Wiki 

A false dilemma, or false dichotomy, is a logical fallacy which involves presenting two opposing views, options or outcomes in such a way that they seem to be the only possibilities: that is, if one is true, the other must be false, or, more typically, if you do not accept one then the other must be accepted. The reality in most cases is that there are many in-between or other alternative options, not just two mutually exclusive ones.
 
False dichotomies are commonly seen in arguments vis-a-vis religion vs. science, and woo vs. science.