Anarchy means "no rulers". By definition, a ruler is a person exercising government or political dominance. There are basically three interpretations of anarchy in use today: individualistic, collectivistic, and nihilistic.
An individualist interprets "no rulers" to mean no political rulers, however they accept that people can rule over themselves and their property. This interpretation is associated with market anarchists and anarcho-capitalists.
A collectivist interprets "no rulers" to mean no political rulers, however they accept that people can rule over themselves, just not their property. This interpretation is associated with anarcho-communists and anarcho-syndicalists.
A nihilist interprets "no rulers" to mean exactly what it says, they accept no rulers, not even of an individual ruling themselves. This interpretation is believed to be the actual meaning of anarchy by people working for or supportive of government.
While the individualist's and nihilist's position is consistent (in the sense that individualism applies "no rulers" definitionally and nihilism applies it regardless of definition), the collectivist's position is not (they take the definitional approach to political rule and the nihilist approach to property).
Why have they not applied logic consistently to either embrace individualism or nihilism? At least with the individualist a collectivist would be afforded some respect. With a nihilist they would be afforded none.