There is a false paradigm of "left vs right" in the way that people think in terms of "left" and "right"

Left to right is a continuum that measures the amount of state control in a polity.

Far leftism, communism, is absolute state control. Control of economics requires state control, so any form of socialism is by definition on the left.

On the far right side is anarchy (pure anarchy, ancap - there is no such thing as a anarcho-socialist, it is a contradiction in terms)

And although the Left has a long tradition of dishonesty and information distortion, which includes anyone opposing them as "right extremists" and changing their own nomenclature, even smart guys like Nolan and Pournelle have contributed to the confusion of definitions of Left and Right.

Much more detail here:
What is leftism? What is rightism? Why are there so many different interpretations?