Private Property is hierarchy. You cannot have an employee/Owner relationship without unjust hierarchy. Personal Property is allowable within Socialism, as such Anarchism is only Socialistic, unless you change the very meaning of Anarchism.

Being able to kill anyone that opposes your ownership of Capital also implies a monopoly on violence, and thus a form of State.

There's no such thing as Anarcho-Capitalism, just Libertarian Capitalist LARPing with Anarchist aesthetics.