Well left/right isn't authoritarian/libertarian, it's collectivist economics/individualist economics.

Authoritarians with collectivist ideals are authoritarian leftists, i.e tankies,

Libertarians with collectivist ideals are libertarian leftists i.e anarchocommunists,

Authoritarians with individualist ideals are authoritarian right, i.e monarchism,

Libertarians with individualist ideals are libertarian right, i.e anarchocapitalism.

Of course there are more examples of ideologies for each quadrant with varying levels of "auth-lib" or "left-right," but just to give you some idea of the differences. There's also auth-lib centers, like National Socialists on the auth side and agorists or anarchoprimativists on the lib side.

Of course judge all of the above groups to your own accord, but it isn't as simple as "left means libertarian" unless you think anarchocapitalism is a leftist ideal, which it by definition isn't.