Although politics is part of our identity - and therefore self-determined - it also depends on our actions. Political philosophies have definite propositional content: dogma, sets of rules. In other words, you wouldn't call Thatcher a communist or Cheney a pacifist, regardless of what they told you.
If anything is part of the dogma of anarchism, it's this: coercion should be avoided whenever at all possible. All the anti-statism flows from two premises, one minor and one major. The minor one is that the state is the primary source of coercion; the major one is that coercion is a bad thing, ethically speaking. Liberals, for instance, don't think that coercion is that bad - in many situations, such as to make a society better fed and educated, they consider it a very positive thing. Anarchists might concede that some goals are worth a little bit of coercion, but they'll do so reluctantly and with a multitude of caveats.
Would you call somebody an anarchist who is pro-coercion? But Philboyd, you say, how might I find such a strange creature? Well, it's easy: look for somebody who professes anarchism but is content to coerce others in their daily life. I'm not talking about, say, Professor Crispy, who thinks some coercion is justified to stop worse coercion (this is a very charitable summary of his position on military intervention). I'm talking about a person who happily abuses their children, or bullies their spouse, or is casually racist. A person like that, despite their protestations, is not an anarchist.
Here's a simpler formulation: regardless of your thoughts on the behemoth that is the State, your attitude to coercion is most easily determined from how you treat those with less power than you. Likewise, whether you are an anarchist or not is most easily determined from your attitude to coercion.
There's a philosophy that's similar to anarchism that 'anarchists' who don't mind coercion might hold. Here it is, courtesy of IOZ: I dislike being rattled by cops; having to buy and take drugs in secret; having to pay taxes; and I suppose that I am viscerally repulsed by wars and the like. Therefore, I am anti-state. Who else is anti-state? Pretty much just the anarchists; therefore, I am anarchist. Note that this philosophy doesn't even try to be ethical; that is, it places no obligations on you to do much of anything. It's an escape clause, a reassuring pablum for the shallow thinker, and I wouldn't in a thousand years call it anarchism.