Even if opportunity were fully equal, a free market would yield some inequality. Opportunities not being fully equal, a free market yields a good bit of inequality. But I think a lot of people get confused and think the free market is the root of all inequality, and that government is the solution. Sometimes, government interference in the economy is the root of inequality.
Samuel Gregg of the Acton Institute makes the case on inequality and cronyism over at the American Spectator:
Crony capitalist arrangements create distinct groups of insiders and outsiders that have nothing to do with classic criteria of justice such as need, merit, and willingness to take on risk and responsibility. All that matters in a crony capitalist world is closeness to state power. If you are, for instance, a young entrepreneur with a new idea, product, or service but lack political connections, you are automatically disadvantaged in such a world. Equality of opportunity is thus undermined. ... There is a price to be paid for all this collusion. By injecting extra-regulatory costs into the economy, undermining the workings of free prices, and shifting economic incentives towards cultivating politicians and regulators, the process of wealth-creation is severely compromised. The result is the type of slow-motion decline that characterizes countries like Italy, Greece, Portugal, and France. That’s bad news for everyone, but especially the poor. The wealthy and the powerful — especially those who rotate between the political, lobbying, and business worlds — can always take care of themselves in a crony capitalist economy. They are crony capitalism’s nomenklatura. But those without power and money are at a distinct disadvantage.
Related: One academic study found that inequality doesn't drag down the economy -- except where that inequality is the result of cronyism.