What is the central tenet(s) of political anarchism? What makes a political philosophy anarchism vs something else?

You can't handle the logistics of a modern civilization without some kind of administration. Someone has to collect, allocate, and distribute resources to the various public services necessary for a functioning society.

There are "anarcho-capitalists" who might claim to want to dismantle all government in favor of totally unregulated capitalism, but that's just trading out elected officials for the private boards of massive companies. Else they temper that private power with "citizen advocacy boards" which, after a long enough conversation with an an-cap willing to earnestly answer questions, eventually develop into something indistinguishable from government.

Government is necessary, anarchists want government without oppressive hierarchies. I say oppressive, because organizational hierarchies are really the only way to quickly and efficiently handle large projects. The problem arises with authoritarian hierarchies, when the scope of hierarchical power expands from clerical to tyrannical.

No they do not want government. If you want a more accurate description of anarchism ask this on the anarchist community.

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"Government" is a very vague term.

Anarchists are opposed to rulers, not rules. We want to be able to establish our own rules directly. The form of social organization depends largely on the anarchist you're talking to, but most of us support some variation on federated communes utilizing direct democracy and delegates, not representatives.

Honestly, just read The Conquest of Bread by Petr Kropotkin. It's available free at thebreadbook.com

E: .com my bad

They want changes to the government. It's like I said bro wants fewer oranges and you said bro wants oranges?