>Can you explain what is wrong with people having different levels of wealth?
There's nothing wrong with it, in moderation. Where it becomes a problem is when the distribution of wealth starts diverging widely from people's expectation of what a fair distribution would be, accounting for different levels of ability and luck. Aside from this cognitive dissonance, there are also pragmatic limits on how big a disparity can be while still having a functional democracy. It's clear that truly enormous disparities in wealth, made even worse by a lack of regulation in political donation, lead to major distortions in the principle of "one person, one vote" which is a cornerstone of democracy.
>Or asked differently, if it is bad, should every individual have the exact same wealth?
No, because people have different levels of ability and experience different amounts of luck. Inequality is inevitable, and the vast majority of people understand and accept that. But they also expect that the system should at least roughly resemble a meritocracy, and that is impossible to maintain in an unregulated capital system because of the feedback loop between capital and income. Most professional sports leagues recognize this problem: once a franchise starts winning, they make more money, which allows them to buy better players, which leads to more wins, etc, until you have a league where a handful of teams can win the championship and the others are perennial also-rans. So they cap the amount of money that can be used for salaries. They are free, of course, to make as much money as they can, they just can't plow it all back into player salaries. Capital is regulated to preserve the fairness of the system. That doesn't mean the teams are all equal, there are still franchises that perform better over time than others. But it's more clearly tied to intrinsic merit like coaching systems and player development, not just going out and buying proven superstars.
Similarly, a person of average skill can get lucky and make a large amount of money. Having that capital in turn makes it easier to make more money. Over time, and across many such situations, capital starts outrunning merit as a predictor of someone's future income, which is socially demoralizing. That's where the US is today: a pervasive feeling that the system is rigged. To a great extent, this widespread perception contributes to the current political climate in the US.