Oho boi it's time to go full wingnut
I have developed a knee-jerk reaction to people using the term 'anarchism', as if the we should be looking for 'The One Program That Will Bring About Anarchy'. Utopia; one perfect -ism away!! I think it's rather laughable to try to systematise anarchy. That is not to say I think discussing it is pointless -otherwise I would be playing Pokémon rather than typing insane prose into my phone- but that I think the search for absolutes and essences to be a flawed one.
Ok onto your question proper; I very rarely use the term 'state' anymore, though that is partly because I don't want to attract bitcoin enthusiasts to any discussion im part of. The other reason is that I'm the sort of contentious asshole to say things like 'I don't believe in the state' or 'the state doesn't exist'. That's not to say I don't see the concept of the state as a useful one. However, I have never touched, heard, or seen 'the state', and I never will; the state is not a corporeal entity even in the way that you or I are, in the way a rock is, in the way a highway is. The state is not the kind of 'object' that 'exists'. To my mind the state is a nebulous abstraction and collection of behaviours, and the beliefs that underly those behaviours. Of course, those behaviours can be horrifically corporeal at times. Nevertheless, I don't think it's possible to discover the essence of the state precisely because I think the categories we apply to devide up the world are modes of interaction derived from culture and experience rather than objects whose essence can be discovered. Note; I probably just haven't done the relevant theoretical homework; who has time for non-fiction?
As usual two veterans have been here before me, and made excellent points far more lucidly than I could hope too. Never the less I will be so vain as to post this as /an/ answer; fear is the mind killer.
Along the lines of funkyanarchy's comment, I focus most on anarchy from the point of view of one person living now -me-, but as I'm sure you've noticed I like to bog myself down with theory and philosophy. And Pokémon.
Now onto your point about anarchists not showing up in response to pharoahs and kings. Whilst this is true in a sense, it is also true that many thousands of people lived beyond these kingdoms and empires -regardless of the many ways these people lived-, and 'wild' spaces filled valleys and rose high on mountainsides. These spaces have all but disappeared, and the people outside have all but been wiped out. Perhaps the all-encompassing nature of the 'states' in recent history has contribute to the emergence of 'internal' attempts to evade and escape control, such as tendencies towards anarchy and other such behaviours? Besides, overworked, hungry, diseased, overtired minds tend not to be the most adept at critical examination. If 'anarchists' had shown up in response to pharoahs, they probably would have been either long gone, or quickly dead.
The critique of 'the state' might be at the centre of 'anarchism', I'm not sure. Perhaps the more interesting question is how much 'anarchism' has to do with anarchy. Is that an answer? Bahahahaha.