Private ownership has led many people to suffer difficulties and face challenging situations without the help of government. Poor people are starving due to the inequality that has been developed. Rich people are becoming more wealthy, while poor people are in a state of misery. Huge investments in capital goods are being made by owners to earn profits, leaving behind the needy people who cannot even get proper food to eat.
Capital, in the sense of the American monetary system, is a source of inequality when it falls under capitalism, or private ownership of the means of production. The means of production are all non-human resources. Private ownership is the ability of absentee ownership. This contrasts with personal ownership, which is ownership of something that the owners actually uses. Private ownership is why there are empty houses and homeless people and large fields of food and people going hungry, just to give a few examples.
The opportunities are not there for those that are born into less fortunate lives. It doesn't matter what you think you know about the American dream, unless you live in an area that cops don't drive through, you don't truly understand what it means to not be equal. Yes everyone has the chance to apply for the job in the paper. But not everyone had the money to go to the school needed to get the job. Capital ownership is power. Power and wealth not only give you a head start in life, they allow you to increase power and wealth throughout while taking away opportunities from others, should you choose to do so.
Let's say you're a capitalist billionaire. You worked your way up through efficient allocation of capital for reinvestment in the economy (helping all who participate). You now have more money than you would ever need. You give money to a worthy cause, naturally.
What capitalism does best, if anything, is to use private incentive to properly distribute capital around society. The government has no self-serving purpose to distribute capital in any particular way, they have a steady income of taxes. As a wealthy capitalist, you may feel better giving to museums and libraries or maybe to college funds or technological institutions or even individual people. Whatever it may be, you are the source of the labor that MADE that money. Therefore, it would make most sense for YOU to decide how it is used. Looking at the lower class of America, whose biggest problem is owning a house smaller than 2000 square feet and only having one car, shows you that a nation needs only 200 years of existence to develop to this point, given that a free market is in place.
The ability to make the effort necessary to own one's own capital is the backbone of the American economy. To take this away is to take away economic incentive. Furthermore, those who own capital find it profitable and edifying to invest in people and resources to grow their equity. This is what creates opportunity in the USA.
Capital ownership is not a source of inequality, but one piece of evidence of the resulting efforts of those more aggressive with their assets. Certainly there are those that started with nothing and have compiled great wealth and capital, while others starting with advantage that have squandered their wealth. Everyone has the opportunity to achieve, but it is often circumstances compounded with effort that challenges some more than others.