Few people think that the political spectrum can be usefully depicted as extending from a “Left” to a “Right.” Ever since the Bolsheviks became fatefully different from the Socialists — about 1903 — it has been apparent that what some people still insist on calling the (overall) Left conflates political forces of fundamentally different values.
But there is another aspect of this sloppy “Left vs. Right” usage that is often overlooked. While “Left” is a term that some political forces use as self-description, “Right” is not. English-language dictionaries do not describe the political connotations of political terms, but the great French Robert tells us under “droite” (‘right’) :
Dans le contexte français contemporain, le mot est surtout employé par des adversaires, se disant de gauche; les partis et le public dits de droite (par les autres) se réclamant en général d’autres dénominations.
In today’s French, the word is mostly employed by opponents, who refer to themselves as being of the Left. Parties and public-opinion tendencies that are called right-wing (by others) generally use different self-descriptions.
So it would appear that the whole Left-Right political usage is primarily one of those who like to refer to themselves as being of the Left. Certainly those who are called “Right-wing” (as in such inexcusable phrases as “the Israeli government is a right-wing coalition”) do not themselves use the term. In other words, while “Left” is often used by political groups — for their own political ends — to describe themselves, “Right-wing” is almost always used as a pejorative, as a term of abuse.