I think you are missing the larger point here. The labels right and left are really irrelevant except to indicate a polarization. Communism and Socialism are classified as left-wing. Fascism shares it's most important characteristic with them; that is simply, state > individual. You could just as easily reverse the argument and say Communism and Socialism are right-wing because they are aligned with Fascism in that idea. In which case you would have to say Anarchy is on the left, because it is diametrically opposed.
The fundamental principle which determines where something falls on the political spectrum is which is supreme, the state/collective or the individual. You can't have Fascism on one pole and Communism and Socialism on the other when their fundamental principle is shared. Ideologies that tend toward state supremacy / collectivism have been historically classified on the left. Those that tend toward individual liberty have been classified on the right. This is what Dinesh is trying, and possibly failing, to illustrate.
