The fallacy of false dilemma (aka black-and-white thinking, false dichotomy, bifurcation, either-or fallacy) occurs when an arguer assumes there are only two exclusive alternatives in a state of affairs, when actually there may be a way for both those alternative to coexist, or there may be more alternatives besides them.

Here is an example:

Billie's Aunt tells her in a scolding voice, "Billie, go take a shower right now or you will be too dirty to go to the theater with us."

This overlooks that Billie may have other ways to get clean besides taking a shower, such as going in the bath tub, giving herself a sponge-bath, or even going for a swim in a nearby lake. It also fails to address whether by merely washing her hands and face and putting on fresh clothes and deodorant, Billie might become clean enough to go to the theater. Unless all of these options are unworkable, the statement is fallacious.

Note that if the statement were modified to be more open-ended, the fallacy could be removed. The following statement is probably not guilty of a false dilemma: "Billie, go do something to make yourself adequately presentable, or it will not be proper for you to attend the theater with us." One must be careful, however. Even this statement could be a false dilemma. For suppose Billie retorts, truthfully, "But Aunt Wilma, I am performing in the play as a haggard vagabond, and this is how I am supposed to look!"

Often this fallacy is constructed so that one of the two options is obviously undesirable (to the intended audience, at least), thereby seemingly forcing the other alternative.

Here is an example of that: ​

A speaker before the United Nations Security Council says, "You must send military supplies to my beleaguered country immediately, or there will be World War III."

In almost every case of helping "a beleaguered country", the UN (or its member nations) will have a variety of options, such as intervening diplomatically, sharing reconnaissance and intelligence, putting economic sanctions against the aggravating party, etc. Unless all such options have been eliminated, the argument is fallacious.

A general template of this fallacy is:

1. A xor B ("Exclusively A or B").

2. B is undesirable (often left unstated).

3. Therefore, A is the desirable choice.