The logical fallacy of false dichotomy or false choice occurs when one provides only two (or a few) answers to a question, giving the illusion that these choices exhaust all possibilities, when in fact they don't. Some examples include:

In fact, both may be wrong. (Also, don't forget that evolution doesn't explain how life arose!)
  • Based on what he claimed, Jesus was either a liar, a lunatic, or the Lord.
This ignores other possibilities, such as "legend" or that he never made such claims that were attributed to him.
  • You're either with us or against us.
I might not stand in your way, but cannot actively support your course of action.

It's worth noting that not all logical dichotomies are false. Consider the etymological definitions of Theism and Atheism.

  • Theism = Belief in one or more gods
  • Atheism = "A" + "Theism" = Lacking + (Belief in one or more gods)

As one cannot simultaneously lack belief and believe, this is an example of a valid dichotomy.