turdas

If you think it's thoroughly left-wing then I think you must not be familiar with individualist and libertarian anarchist thinkers. I don't think free-market anarchism involves much social production for example. In American political theory anarchism is what gave birth to libertarianism, which is pretty much a right-wing ideology.

The political compass has both an X and a Y dimension, you know. As it happens, the Y dimension exists almost specifically because of anarchy.

Secondly, I'm not referring to what the random person thinks anarchy is, but what actual anarchists believe, and among anarchists anarcho-capitalism is fringe, and an offshoot of liberalism.

You're doing the monopoly thing here again. When by "anarchist" you refer exclusively to left-leaning anarchists, of course anarcho-capitalism is going to be fringe among them.

Not to mention the fact that free-market anarchism is a distinct ideology from anarcho-capitalism and, to my understanding, much less fringe among self-described anarchists. The primary distinction seems to be that anarcho-capitalism exists at a lower energy state, a sort of a decay product that free-market anarchism would likely almost immediately decay into upon contact with the real world.

Plato having talked about anarchy at one point doesn't suddenly mean that the entirety of anarchist history suddenly doesn't matter.

One ideology misappropriating the term also doesn't mean that all other meanings of the word suddenly don't matter. Don't get me wrong, I sympathize with many of the ideas of left-leaning anarchists, but they do suck at naming things. When the same concept covers both extreme right-wing libertarianism and extreme socialism, you really should be qualifying it with something to avoid confusion.

This is a pretty biased way of putting it. The concept of anarchy predates the interpretation used by modern left-leaning self-identified anarchists by a couple of thousand years. In online circles such anarchists often seek to monopolize the term (like you are doing right now), but they factually weren't the ones to coin it; when it was originally coined by Plato, nobody had any idea what the fuck capitalism or socialism even are, and in fact Plato used it as a cautionary example.

I am guessing your gut reaction will be to recoil at this grave attack on your ideology. I implore you to stop and consider that most people are not in fact at all familiar with left-wing anarchism as defined by Proudhon etc., but are vaguely familiar with the concept from many other sources. Therefore when you talk about anarchism without a qualifier to mean anarchic socialism, most people will assume you are talking about some Mad Max law of the jungle nonsense and then summarily dismiss anything you say as insane rambling.