The first abstract mathematical differentation made by the prehistoric human beings was probably the differentiation of one and two, which makes Two the oldest mathematical concept known to mankind.
Many cultures have very strong relationships to the number two. Two is the perfect number, and everything must come in pairs in order to stay intact. Odd numbers bring bad luck because they cannot be divided in two equal halves. If twins are born, they are considered sacred, more perfect than their "non-doubled" tribemates.
Languages still exist which numerate in a "primitive binary system", combining all numerals from two words - "one" and "two".
The simplest possible choice that bears information is the choice between two options. One binary choice bears one bit of information. The bit is atomic - it cannot be subdivided.
The human brain has a natural tendency to simplify all classifications down to a single binary choice. In the human society, it is much more common to see a competition between two factions than between three factions.
Some religions and other ideologies embrace a strong partial dualism - typically, by classifying each thing to either "good" or "evil". This kind of thinking leads to an extremely twisted view of the world which tells far more about the defects of the human brain than the nature of the real world.
The Rule of Three and Hypercosmic Logic are ways for transcension of dualities.