In a libertarian society, everyone is equal under the law. No one can manipulate the laws for his own advantage. No one has any interest in fighting each other for a power that does not exist. This is not a utopian goal : it's called the rule of law. It's called equality under the law. This ideal was explicit - although incompletely implemented - in the American Constitution and other constitutions.
In practice, democracy and big government has eroded a lot of the equality that we are all owed. We are all human beings, but unfortunately the statists and their ruling classes make some of us into inferiors and others into superiors.
A common criticism of capitalism is that the "rich get richer and the poor get poorer". That's almost half-right : most rich people do get richer. Due to bad decisions, some rich people lose all their fortune (I still remember a friend of my father's who went from multi-millionaire to penniless). Success is never assured.
Of course, what the statists actually mean is that capitalism breeds inequality. This assertion is, in fact, trivially true in one sense. Obviously, the more prosperous a society is, the more resources will be available, and the more resources that will be available to those who contribute the most.
Sports players, for instance, draw in millions and millions of dollars' worth of entertainment money : they give tremendous leisure resources, and thus are rewarded by the market much more than they were 10, 20 or 50 years ago. So there will always be a growing disparity between the most productive and least productive in a prosperous society, simply because of the Bell curve.
There is a more important sense in which the assertion is simply false. In most economies, including statist systems, there are two classes of citizens : the slaving class and the ruling class. There is little movement between these two classes, except the movement necessary for the ruling class to cull out its bad sheep and replenish its ranks. The only way left for people to claim what is rightly theirs is war.
