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> Anarchism is anti discrimination (pro egalitarianism)

Anarchism is anti-state. That's it. Everything else is anarcho-something.

That's not true at all, anarchism is anti-hierarchy. The state is just one (and the second most prominent) hierarchy that anarchists oppose.

>anarchism is anti-hierarchy

Anti-involuntary hierarchy, not those who voluntarily take part of certain types of power hierarchies.