People aren't selfish or greedy. People are ambitious and in the current society those people are raised to believe that to be the best you have to be selfish and greedy. They aren't traits you are born with, they are learned.
But anarchy still is the best way to deal with greedy people as any kind of hierarchy will just allow the greedy people to get to the top. Hierarchies don't punish the greedy, they elevate them to the highest positions in society as those that aren't concerned with other peoples well being can always find a way to gain authority over them.
There needs to be something to try to prevent and/or punish that.
Anarchy has that something. You can counter abuse without being abusive yourself. We can build social structures that prevent greed without hierarchy. The solution isn't to give some people a monopoly on violence because that position will always attract the most violent. It's to build a social networks that sees problems before they happen and provides support. Punishment isn't a productive method of preventing harm. It's vengeance, not prevention.
What is currently destroying the US isn't libertarianism, it's bad education, mass media manipulation and a bunch of people following orders.
Learn some history
OK
https://en.wikipedia.org/wiki/Revolutionary_Catalonia
https://en.wikipedia.org/wiki/Paris_Commune
https://en.wikipedia.org/wiki/Makhnovshchina