Another problem with this grid is that authoritarian and libertarian are both loaded terms and not opposites of one another.

Many people take "libertarian" to mean unfettered laissez-faire/neoliberal capitalist economics - which is a fundamentally authoritarian so long as people within those structures depend on wages and insurance plans for survival and are beholden to contracts; a CEO without red tape is therefore no different from a mini-dictator. Anti-authoritarian measures to regulate the power of corporations are also anti-libertarian. Laws which prevent corporate monopolization are also anti-authoritarian and anti-Libertarian.

The opposite of authoritarianism is not libertarianism, it's anarchism.

Historically, "libertarian" was a synonym for anarchism or the libertarian branch of socialism. In most places it is still used that way, and even in the United States where right-wing liberalism has appropriated the "libertarian" label to an extent that older sense is also still used. 

The first "libertarian" was Joseph Dejacque an early communist anarchist who used the word to circumvent anti-sedition laws in France which prohibited the use of "anarchist." 

I would say the workplace is a very important part of everyday life for many people so they do have the kind of authority on each of their microscales to be authoritarian. Hell they are authoritarian by virtue of their structure aka owner, board, manager, workers, etc. 

Again, not authoritarian by the political definition. This is about politics, not sociology or philosophy.

If you want to take it broader I could even say my hobbies are authoritarian because I would literally die from depression if I didn't have them, so they are commanding me to do them.

I think it is by the political definition. Economics and Politics are linked very closely

Yes, but a corporation is not a government and has exactly zero authority. Not over politics or over people. Authority is given, not implied. No one has given authority to corporations and a singular corporation is not needed to govern and can be easily replaced. A governing body is different.

Please don't try to take this further. This is simply about the definition of authoritarianism. I'm not really in the mood to philosophize what authority is.

Free speech is most definitely a left wing value. Ask Noam Chomsky or Prof Richard Wolff. I'm a true blue lefty and I'm very much pro free speech.