Right-wing and left-wing are terms that entered political parlance due to the seating arrangements of the 1789 French Etats Generaux. Venues and seating arrangements changed, (even going so far as to devolve into numbered seats drawn by lot in an attempt to break up any special interest groups) but the distinction between the nobles and pro-monarchy forces seated at Louis’ right, and the more radical bourgeoisie seated on the left maintained.
Out of any given pair of opposites, there will be a general consensus as to what category it “belongs”: past/future, stable/chaotic, conservative/liberal, hawk/dove, rich/poor, industry/nature, reactionary/revolutionary, male/female.
Note that I do not say that there are no right-wing women, or left-wing hawks. (Or turkeys, for that matter). It just seems, in the West, as inheritors of an Aristotelian system of classification, we have a tendency toward binary bifurcation.
(There are two kinds of people in the world: those who split the world into two kinds of people, and those who don’t.)
There are other possible cleavages proposed by those with other axis to grind. Libertarians claim state control versus individual choice is the most significant cleavage; Greens claim the protection of the environment is the great divide.
Others (foreigners, most likely) recognize this left/right split as being far too simplistic, and have added additional axis, but it comes down to a slightly more sophisticated version of the same thing.
You ain’t got no friends on the Left (That’s right!)
You ain’t got no friends on the Right (What’s left?)
-Firesign Theatre