Upvote:-1
There are always (ok, nearly always) conflicts within a culture. Your problem is seeing them as simplistic dichotomies, when there are many different sides. For instance, in the US the right as represented by the Republican Party is (over-simplifing considerably) divided between the economic & political conservatives and the cultural conservative/religious right, who often espouse economic policies more suited to the left. Then on the left/Democratic Party side you have everything from traditional liberals to outright socialists like Sanders and Ocasio-Cortez. And outside the non-dichotomy of the two major party system, you have everything from Libertarians to Greens.
Upvote:2
Insofar as I'm aware, the left vs right dichotomy specifically dates back from the French Revolution, during which conservative royalists sat right and liberal republicans sat left.
Dichotomies within societies, on the other hand, are much older. As early as Ancient Greece, (one would presume conservative) elders were railing about (presumably more progressive) youngsters owing to their lack of deference to traditions as explained in the answers to this question. And as pointed out in Mark's comment, there's no reason to assume it's not older.