Earlier quoted context omitted.
Oxford dictionary: noun belief in the abolition of all government and the organization of society on a voluntary, cooperative basis without recourse to force or compulsion. That sounds compatible with mere free trade amongst men without any sort of socialism. Seems like leftism wants some involuntary reallocation of capital, but maybe I'm mistaken. If they don't I'd say they're just charitable capitalists.
Anarchism isn't just "no rules or government" as it means in common parlance; it is against coercive hierarchy in general, and capitalism is inherently coercive because it involves denial of access to means of production, and denial of access to necessary resources like food and medicine. Think of anarchism as being more akin to a modern attempt at the tribal system of humanity's prehistory, but scaled up: resources…
Or say I have a full fledged industrial scale wave soldering, mass PnP, full inventory of millions of dollars worth of components. I need it to feed my family, I'm not going to just hand it to you after I gained it through consensual trade fair and square. Doesn't that require coercion? I'm not just going to give up my goods I worked hard for, what's going to happen when the comrades see the loaded barrel of a rifle protecting that which feeds my family? I think a lot of people needing to feed there families are going to have a lot of rifles, and they're not going to be very happy about someone coming along to "open up access" to means of production of their business.
When you take my means of production, you deny ME access to what I gained without coercion, by using coercion.
This all just sounds like a violent way of less efficiently allocating capital, under the guise of non-coercion. Access to property should require consent, otherwise you have coercion. Seems to me free market trading of private property fits a lot more neatly with the oxford definition of anarchism.