Nothing at all is wrong with inequality. And someone else being rich doesn't make me poor.
Most people think of wealth purely in terms of creature comforts. But that doesn't apply to extreme wealth. Above a certain threshold, additional wealth doesn't change a person's lifestyle much. That additional wealth is experienced as economic power. People with lots of wealth have more power to direct labor and resources. And the simple truth is, most people don't want that kind of power and responsibility - not enough to spend their lives pursuing it.
I see nothing inherently wrong with economic power being concentrated by people with the skill and the ambition to use it effectively. That's the whole point of capitalism really, to reward those who use wealth successfully with more wealth, so they can do more good things with it. And, on the flipside, to remove wealth from those who squander it.
Most of the complaints about wealth inequality are coming from people who want the government to have more power than rich people. But our country was designed to do the opposite - to keep most power in private hands and not under the direction of government.