The bifurcation fallacy is committed when a false dilemma is presented, i.e. when someone is asked to choose between two options when there is at least one other option available. Of course, arguments that restrict the options to more than two but less than there really are are similarly fallacious.
Examples
(1) Either a Creator brought the universe into existence, or the universe came into existence out of nothing.
(2) The universe didn’t come into existence out of nothing (because nothing comes from nothing).
Therefore:
(3) A Creator brought the universe into existence.
The first premise of this argument presents a false dilemma; it might be thought that the universe neither was brought into existence by a Creator nor came into existence out of nothing, because it existed from eternity.
Another example emerged when George W Bush launched the war on terror, insisting that other nations were either for or against America in her campaign, excluding the quite real possibility of neutrality.
Complex questions are subtle forms of false dilemma. Questions such as “Are you going to admit that you’re wrong?” implicitly restrict the options to either being wrong and admitting it or being wrong or not admitting it, thus excluding the option of not being wrong.