"Anarchism is actually the belief that people can live peacefully among one another and aggression is not needed unless you or someone you know is physically attacked."
Surely I can use aggression if someone eats my banana, even if they haven't "physically attacked" me. You can't have industrial civilization if people can't defend their property.
But then it all starts to fall apart. To know whether aggression is permissible in some instance, you need to know whose property was involved. For example, if I believe that Democratically-passed tax laws make the money you owe in taxes no longer your property, then not paying taxes is impermissible aggression.
So this really reduces to "anarchism is actually the belief in absolute individual property rights". But you can't really have such a thing without some particular theory of such rights. So how does a person acquire a right to property?
If, for example, I believed that all humans have an equal right to all property and if you want exclusive use of property, you must buy it over time from everyone else, my understanding of what constitutes aggression is going to be radically different from yours.
Practically nobody believes it's right to use force to take what you are not entitled to, we disagree over what people are entitled to. And it's dishonest to say that your position is the one that means we don't use force to take what's not ours because almost everyone will claim that's true of the system they advocate.
I did not once mention that property rights do not exist I simply gave a brief summery of what anarchy is and what it means to be an anarchist. I do not need to go into every detail of every corner of the ideology to explain what anarchy is.
You are right in the sense that you have the natural right to defend your property with the use of aggression but what you do not have the right to do is aggressively attack another's person or property. The government has a tendency to do this most often. Why should government have different rights to everybody else?
By saying that the act of aggression would be continuous under an anarchist society is pretty much like saying that everyone is a crazy lunatic socio path wanting to kill everyone and everything in it's path, which in hindsight couldn't be further from the truth.
Thank you for this pretty enlightening comment.