[OkayPhysicist]

Left and right are useful labels, and while the exact border may be somewhat ambiguous or perhaps arbitrary, they do identify a useful spectrum. Ultimately, left vs. right-wing thought boils down to views on hierarchical power structures. On the extreme right, there's the view that hierarchies are good and natural, and should be reinforced and expanded. On the extreme left, there's the view that hierarchies are evil and unnatural, and should be abolished. In between you have a whole spectrum of views like "some hierarchies are a necessary evil", "some hierarchies are good", etc.

Individual issues sometimes unambiguously map onto this spectrum: Supporting slavery (a pretty obvious hierarchical construct) is further right than wanting to abolish it, for example. Other times, issues occupy some certain space on the spectrum, with opposing viewpoints on both sides of it: a left-leaning individual might oppose free-market Capitalism because it forms a hierarchy of wealth, while a further right-leaning individual might oppose Capitalism because it gives the "wrong" people higher standing than they should (according to some other "better, more natural" hierarchy).