so I take my neighbor to court to try to get some of his cash
As your neighbor, I wouldn't go anywhere near your "court."
Of course, the outcome would be determined by a judge, jury, or some similar arrangement.
As a consequence of my previous response, your judge would have no authority over me.
Then the defendent would be forced to hand me the money or else suffer some consequences.
It is possible that in certain situations, people will steal from you, especially if you don't have any defense against them. Part of what makes someone an anarchist is understanding that this is always the reality. Someone might try to steal from you. You just have to consider whether you want that someone to be the monopoly master of violence...or not. At least in the situation you described you are allowed to try to resist. Now you can't.
In addition, I don't think that this company would last very long trying to loot other people. The costs of raiding people's houses would be too prohibitive, and even the most radical communists wouldn't be able or willing to part with the resources needed to keep this going.
So 1) It's not going to happen, because realistically, there are far too many obstacles...2) Even if it could, it's a risk I'm fine with, since it's better than the certainty
I'll be stolen from now.
The question is, is such an oppressive condition inevitable? Does it naturally arise periodically as cultures meander through various guiding philosophies? Is it inhernet in human nature that there will always be a majority willing to plunder each other?
Three questions, three answers
1) No, but it's likely there would be pockets of it for a long time, even if there was an anarchist revolution.
2) It has, but doesn't necessarily have to.
3. No. It's inherent that people are self-interested, but it's possible to have a society where self-interest is voluntarism.