Economic inequality is a problem because it undermines our economy and our democracy. High levels of economic inequality make the US economy fragile, and perhaps unsustainable. Our economy is built on consumer spending, which accounts for about two-thirds of our economic activity. However, the rich don’t spend as much of their incomes as those with lower incomes do. They save more, they invest more (including in speculative investments that add no value to our economy), and they save, invest, and spend overseas, which does not support the American economy. Envision the difference between a) a large corporation’s CEO or a Wall St. hedge fund manager taking home $100 million for a year’s work and b) 2,000 middle class families taking home the same $100 million, which would be $50,000 each (perhaps in unemployment benefits or to support continued education). Which income distribution is going to result in more spending in our local economies and more support for local businesses, their employees, and their suppliers? Which income distribution is better for American workers and businesses, or in other words, for the US economy? 
The 90% of us who aren’t wealthy have a smaller and smaller share of the income and wealth of our society. Therefore, we simply do not have the consumer purchasing power needed to keep our economy running at full speed. Without sufficient demand for consumer products and services, businesses reduce production and lay off workers. This ripples through the whole economy as these laid-off workers don’t have money to spend in their local economies. Furthermore, related businesses feel the downturn, including the companies that build the equipment that manufacturers of consumer goods use, those that transport the goods, and those that build and furnish the buildings that house consumer businesses. As a result, unemployment (and under-employment) increase, and a vicious cycle of declining prosperity ensues.
There is also a political dimension to economic inequality. The wealthy donate money (and lots of it) to candidates for elected offices. Therefore, elected officials hear the voices of the wealthy much more loudly than they do the voices of lower income voters. As a result, policies tend to favor the wealthy, such as cutting their taxes, including the estate tax, income tax rates on high incomes, and corporate taxes (especially for large and multi-national firms). These tax cuts mean government has less revenue to spend on safety net programs and for investments in basic infrastructure such as education, mass transportation, and roads. Furthermore, many of the well-off advocate for cuts to safety net programs that support stability, if not opportunity and upward mobility, for those working in low paying jobs or facing adverse circumstances such as loss of a job or a health crisis. Therefore, economic inequality begets political inequality that begets even greater economic inequality.
Inequality and lack of social mobility are intimately linked; we can’t increase mobility and opportunity without reducing inequality. Those with low income and wealth simply are unable to make the investments in themselves, their children, and their neighborhoods that are needed to foster mobility and opportunity. In addition, unequal political power perpetuates and exacerbates economic inequality. As a result, the ability of the middle class and poor to build better lives for themselves and their children has become very limited indeed. 
 Reich, R. (2010). “Aftershock: The next economy and America’s future,” Random House books.
 Bernstein, J., & Spielberg, B. (6/5/15). “Inequality matters,” The Atlantic