I'd like to point you to a detailed rebuttal of this claim in text [1] and video [2] form. Wikipedia should not be anyone's only source.
[1] https://springtimeofnations.org/2021/04/yes-ancaps-are-anarc...
Re:Pëtr Kropotkin and Mutual Aid
by ZeroGravitas on Saturday November 05, 2022 @02:55PM
(#33484473)
Having an obscure historical claim to a word commonly associated with people who you disagree with is the best kind of Technically Correct, but not great for communication.
I was mostly trying to point out that there are disagreements about what "anarchist" means and avoid confusion.
Your comment seemed to echo that, talking about some Anarcho-capitalist libertarian ideal buzzword society, linking that to his anarchism and then further attaching the generic word 'capitalist' to it.
This felt like a stretch.
https://en.wikipedia.org/wiki/Anarcho-capitalism
> Anarcho-capitalism is also distinguished from anarchism, an anti-capitalist movement that opposes unnecessary coercion and hierarchy, and social anarchism, a branch of anarchism that sees individual freedom as interrelated with mutual aid. Unlike anarchists, anarcho-capitalists support private property and private institutions. Anarcho-capitalists also reject the libertarian socialist economic theories of anarchism, arguing that they are inherently authoritarian or require authoritarianism to achieve, while believing that there is no coercion under capitalism. Despite its name, anarcho-capitalism lies outside the tradition of anarchism and is more closely affiliated with capitalism, right-libertarianism, and liberalism