The fantasy-story of right-wing anarchy is creating misinformation, someone thinks that something like “anarcho-capitalism” is real philosophy, instead of the linguistic distortion of fascist-capitalism that it is.
Should people even specify that they are left-wing anarchists now? Do we really want to put a stop to this propagandistic joke? Anarchy will always be the extreme left into the political pendulum.
And I will tell you more: anarchism is by its nature also pacifism, as it aims to prevent any form of uncontrolled power on others. This is to silence even centrists: another fake group, people who think that it’s not “extremist” in its own abstinence, in delegating violence.
The term leftist is considered to come from the fact that people sitting on the “Left” in the Estates General in France. Generally, liberals, (Jacobins, Third Estate). There is very poor sourcing for this online, but Wikipedia cites some untranslated difficult to source french book.
In mainstream discourse, “left” takes on a number of meanings, but to the extent that left is meant to mean anti-capitalist, and/or, Marxist, anarchism has left wing currents, hence, left wing anarchism.