> coercion is not a requirement for governmentThen you and I are defining the word "government" differently. What I am arguing against is coercive enforcement of rules. You can call it whatever you want; if you don't want to call it "government", then let's just avoid using that word at all so we at least know what we're talking about.
> what happens if I don't agree with a rule. And then I break it? If there is some sort of punishment, then there is coercion
Then, once again, you are giving different meanings to words than I am. "Coercion" as I am using the term means forcing people to do things they would not voluntarily choose to do. Letting people voluntarily choose to do something, in the full knowledge that they will suffer consequences, and then imposing those consequences, is not coercion.
Also, you use the word "punishment", but I haven't used that word. I have not talked about throwing people in jail. I have only talked about things like refusing to interact with someone. Unless you are going to claim that you have a right to have other people interact with you, no matter how much of an asshole you are, then I don't see how you can call it "coercion" when people refuse to interact with you because you refuse to regulate your behavior in order to facilitate cooperation.
Violent consequences are a more complicated matter, yes, but (as is discussed, for example, in Friedman's book) there is still a key difference between violent consequences from private entities (who have to weigh the possibility that they will in turn be targeted by violent consequences from other private entities) and violent consequences from governments (which do not suffer any consequences in turn, because they are allowed to do things that would be considered crimes, at least on their face, if private entities did them--in fact, this is how Friedman defines a government).