Income inequality is a red herring, and too often it is chanted without any thought given to what support for equality means or why inequality is ostensibly opposed. There are, of course, two classes of reasons that people have for supporting income equality.

1. opposition to income inequality per se

2. opposition to something other than income inequality, with inequality as a proxy for that thing

For (2), the person may either believe that income inequality necessarily results in the problem they're concerned about, or they may be confusing it with inequality per se.

For (1), one motivation is the classic envy of the have-nots for the haves, or a basic confusion about justice where it is misunderstood as entailing equality.

The first real problem is poverty. A double income upper middle class family with a $600k home is not equal to the millionaire or billionaire down the road in terms of income, but they are not suffering because of that inequality. Furthermore, the easiest form of equality is universal poverty, something socialist/communist regimes were quite good at arranging. Obviously, this kind of equality is undesirable.

A second problem is the influence money has in politics. This isn't the result of inequality per se, only the deranged relationship to money that people, including those in politics, have. The lust for money is the real culprit here, not money per se.

A third problem, related to the first, is one arising from ineffective markets. On the one hand, this might be the result of central planning or onerous regulation and other features of economies in collectivist societies. These can crush personal initiative and responsibility, and reduce the individual to an element of the collective, thus diminishing the dignity of the person. On the other hand, while free markets are quite good at allocating goods, they aren't infallible, and an idolatry of the market can encourage a participation in the market that flouts morality and regard for human dignity, resulting in a market that instead of contributing to the freedom and good of its participants, becomes a force for exploitation in which some enrich themselves through unjust practices. (I would also add a radical, totalizing libertarianism ideology that reduces the human person to an economic actor - full stop - and construes all human activity as economic, thus dehumanizing market participants.)

I would encourage people to read JPII's 1991 encyclical "Centesimus Annus" for a balanced summary critique of the dominant economic orders of the last century or so as a corrective for their errors.

[0] https://www.vatican.va/content/john-paul-ii/en/encyclicals/d...