Let's get weird.
Morality is defined on a person to person basis. There isn't a real scale to measure what's fair and what isn't, and while you can argue that, you'd be arguing about it constantly. I think the fatally flawed assumption here is that society cares about you, or more importantly, about equality. It doesn't. At the end of the day, the only thing that matters about the system is that it works. It does! Having to compete with each other for the chance of extreme wealth creates more rewards for exploring new ideas and advancement than working for "the greater good" would. If human beings weren't as selfish and greedy at heart as they are, perhaps things would be different. As it stands, altruism is incredibly rare. Those kinds of actions require incentive.
The downside is that this leaves some people unhappy. Many are bitter, many feel cheated, and many more still don't have time to worry about feeling either of those things because they're just trying to get by. Some of these people band together, they push for change - they appeal to the politicians and the people as a whole to be more inclusive in favor of giving more people a chance to rise up. This isn't a bad thing by any means, but lets be honest here. These people are comrades by circumstance. Given the chance to rise up on their own, almost every individual would leave the group behind. People for the most part don't care about society really, just as society doesn't really care about them. What matters is that everything works. In the modern west, we're taught from a very young age that we matter. We grow up with a sense of self importance that doesn't really mesh with the reality. I don't matter, you don't matter, and the only way you're going to get anywhere is if you pick yourself up and carry your reluctant fleshy vessel there yourself.
TL;DR - It's not wrong that the poor stay poor and the rich get richer, because that assessment relies on the assumption that everyone deserves something. Nobody deserves anything.
Got the cynicism out of me for the day, sorry folks.