I haven't seen much on this site indicating that anarchism equals communism, at least not from most of the regular posters - myself included. Historically, anarchism has been part of a broad socialist tradition, but there have always been anarchists who were not interested in socialism, or in any other specific economic arrangement.
The socio-economic system that existed in "Russian history" (I'm presuming you mean 1917-1989) was called "communism" by its partisans and pro-capitalist enemies. But how accurate of an analysis was that? Not very; critics to the left of Leninism referred to it either as "state communism" or "state capitalism" depending on their particular analysis of capitalism.
Don't know where that quote you cited comes from, but it sounds like it could have been written by David Hume or John Locke, neither of whom was much of an anarchist. There are tons of assumptions behind the terms "freedom," "will," and "infringe," and almost all of them are wedded to the history of bourgeois economics and philosophy. As such, they don't have much to do with principled and critical anarchist discourse.
And "man" doesn't begin to describe the whole of humanity...