The origins of the terms left and right were explicitly authoritarian vs democratic.

The split dates to the summer of 1789, when members of the French National Assembly met to begin drafting a constitution. The delegates were deeply divided over the issue of how much authority King Louis XVI should have, and as the debate raged, the two main factions each staked out territory in the assembly hall. The anti-royalist revolutionaries seated themselves to the presiding officer’s left, while the more conservative, aristocratic supporters of the monarchy gathered to the right.

The right has spent the centuries since trying to pretend that the left can also be authoritarian and still be the left.

Hell, the economic left, communism, was only relegated to the left, because it was a democratization of the economy. The goal of every man being truly equal. You labor, but you also partially own the factories you labor in.

Lenin took this dream, and betrayed it. He turned communism from a force of equalization into a new feudalism. You labor for the good of the state and own little to nothing of it. Stalin then stepped in as a new despotic king.

This makes the communism of Lenin and Stalin a very right-wing thing. Both of them actually snuffed out true communist movements, first Lenin in Ukraine, and then Stalin in Hungary, Which is how the term Tankie was born, the Tankies supported the soviets sending in tanks to put down the communist uprising in Hungary. The people just wanted to be able to vote, which is key to actual communism.

Then you had Mao. He was not as petty and cruel as Stalin, but made up for it with gross incompetence. His brain-dead orders caused millions to starve, all while he never had an empty stomach. Because while all animals are equal, some animals are more equal than others.

Mao also put down actual communist movements as a threat to his power.