Left is literally the opposite of authoritarian. You seem to be conflating a whole lot of ideas and terminology here. You sound like an ideological leftist who has been confused by the right's deliberate language-muddying.
Left is egalitarian. That takes many different forms: socialism, communism, direct democracy, anarchism, etc.
Right is authoritarian. That also takes many different forms: monarchy, feudalism, oligarchy, corporatism, etc.
Authoritarianism (or vertical/hierarchical power structure) is THE defining characteristic of the right. "Auth-left" is Doublethink; an oxymoron meant to distract from the fact that wealth and power are one and the same.