“I think makes more sense to define left and right as
left — generally egalitarian and/or libertarian, e.g. anarchism, classical liberalism, geolibertarianism, and so on
right — hierarchical and authoritarian, e.g. absolute monarchism, fascism, or Juche”
Well if you make up your own meanings for words, no-one else will be able to understand anything you say.
The Left (Socialism) is for collectivism, so has no time for individual freedoms, and has to be authoritarian to confiscate all private property, and force people to work to their assigned tasks in a centrally planned economy. Before Socialism came along, the nearest thing to a Socialist Dictatorship was the Feudal system of absolute Monarchs. These don’t really exist any more, so Socialism and Fascism are now one, just with the King replaced by the Party Chairman as absolute ruler.
The Right (Capitalist Free Market) puts individual freedoms before government control, so is is favour of small government, low taxes, and self-reliance. It is the right that tend towards Libertarian philosophy, and at the extremes (No Government, absolute Freedon) would be anarchy.
No wonder we can’t agree while you define your terms back to front!
“left — generally egalitarian and/or libertarian?” What are you thinking?
The left promotes egalitarianism as equal outcomes for everybody, whereas the Right promotes egalitarianism as equal opportunities for everybody, with the smarter and harder working doing better than the stupid and lazy.
Libertarian: a person who upholds the principles of individual Liberty especially of thought and action. You will find it very difficult to find anyone on the Left supporting Free Speech, Freedom of action and Freedom from Taxation. The Right are about individual freedom, the left are about Government control of everything.