The problem with conventional approaches to the left-right political spectrum is that they either fail to define the alternatives in question, or proceed to define them in terms of non-essentials.
One common approach, for instance, fails to specify the precise nature of either side, yet proceeds to place communism, socialism, and modern “liberalism” on (or toward) the left—and fascism, conservatism, and capitalism on (or toward) the right.
This makes no sense, at least in terms of the right. Capitalism—the social system of individual rights, property rights, and personal liberty—has nothing in common with conservatism or fascism. Take them in turn.