I'm telling you that you're running into extreme absurdities. I have more personal freedom in a socialist society, where my needs are more assured, than I do in capitalist society, even if said capitalist society was more of a nightwatchman state. By making "authority" purely about how the state treats anyone, and removing all economics from the equation, you create absurd contradictions. That's why class analysis is important.
The political compass makes no sense. It's sole purpose is to affirm liberalism by pretending there's a spectrum of libertarian to authoritarian, when such terms are utterly meaningless when looked at without understanding class. What matters is who is the state serving, how, and why, not if the state is mean or if the state is nice.