It's simple math: in order for a few people to be rich, everyone else must have much less wealth. That's all there is to it. Creating a wealth gap so some can be rich necessarily means that almost everyone else must be poor, or at least not rich. You can never get out of that equation in that economy, no matter what tricks you try. The system requires a vast supply of poor people to use as props. If you're not rich, it isn't because of some personal flaw, it's because you live in a system that makes most people unrich to enrich a few.
An egalitarian society has a much narrower range, and thus, nobody is really rich or really poor. The democratic-socialist states in Europe tend to do this, and it works pretty well -- they're some of the happiest countries with high quality of life. The high taxes cover the essentials, like health care and education, so you don't need a lot of money left in your pocket because most of what you still have left to buy is extras.
It also depends on the type of your economy, of course. Above I'm describing capitalism. In a gift economy, rich is defined not by what you have but by what you give away. So there are more ways to be rich. A skilled hunter who takes food to the grandmothers, a widow who tends other people's children, a talented beadworker helping others with their regalia -- all rich. That guy hoarding everything for himself? He's poor, and people feel sorry for him that he never seems to have "enough" to give away. In a gift economy, it is considered shameful for anyone to have too much when others go without. You don't let that happen. If you see someone hungry, you feed them. And then when you come home soaking wet with no deer, somebody feeds you.
Always aim to know how the system works. What people say about it isn't necessarily the truth.