Part of the problem is that people use different measuring sticks for their definitions of "left" and "right." If your "right" is my "up" then how do we reach a common ground to discuss things?
I may not have the typical view of such things, but I don't see this as a "one straight line, two extremes" type of thing. More like three segments sharing a common central point. One one extreme is individualism... capitalism. On another extreme is facism, and on another is communism.
Say you start at the communist extreme, and move towards a more central position. You are moving towards facism and capitalism. At some point though (the central point), you have to make a decision. Continue towards the individualist capatilist extreme, or set your course to the socialist facist extreme.
Both facism and communism are socialist extremes (collectivist). Neither is truly individualistic, thus neither is right wing. It's almost as if liberals want to say "if you're not leaning towards communism, you're leaning towards facism" which is ridiculous. There is another option.
I've always felt the "left" and "right" labels were limiting, but I think that's because people inherently mix economic and social organization when applying such labels. You can put social organization on a straight line, with collectivist on the left and individualist on the right, but when you include the economic aspect it really complicates thing.
The big liberal fallacy, IMO, is that they believe facism begins on the right end of the social spectrum and diverges from a democratic capitalism on economic grounds. In reality, it starts on the left end of the social spectrum and diverges from communism on economic grounds.
IMO anyway. I don't tend to think of these things in the typical manner, so perhaps I'm just insane.