The "authoritarian" left is just the framework of every revolution that actually won. There is a very special kind of Western detached romantic chauvinist "left" that believes only in failed and failing pure leftism and tragedy and is shocked and outraged at what it means to win, to establish defenses, to keep a nation or nations running.
There is no liberal left. Liberals are the mainstream political and are by definition conservative under global capitalism.
Depends a lot on where you live. In many countries, communism is simply considered "radical/violent" rather than "authoritarian", and one is not considered a leftist of any sort unless they defend a leftist stance on the economy (progressive views on social issues may not be described as leftist everywhere).
To be clear, you were saying Capitalism is left wing. They are using Liberal, as in Libertarian, not as in the actual meaning of Liberal as in Capitalist.
A lot of people who claim to be liberal, just aren't left wing. The good example is the FDP party in Germany.
To quote Wikipedia:
The FDP's political position has variously been described as centrist, centre-right, and right-wing. The FDP has been described as liberal, conservative-liberal, classical-liberal, and liberal-conservative. Other sources have described the party as libertarian or right-libertarian.
There are left wing liberals, but don't act like they usually call themselves liberal.