Robin Hanson notes insightfully:
As I noted a year ago, inequality discussions focus almost entirely on the smallest (#6) of these eight kinds of inequality:
  1. Inequality across species
  2. Inequality between actual and possible humans
  3. Inequality across the eras of human history
  4. Non-income inequality, such as of popularity, respect, beauty, sex, kids, political influence
  5. Income inequality between the nations of a world
  6. Income inequality between the families of a nation
  7. Income inequality between the siblings of a family
  8. Income inequality between the days of a person's life
Humans clearly do not have a generic aversion to inequality; our concern is very selective. I suspect our distant ancestors often formed coalitions that complained about inequality of transferable assets, as a way to coordinate a veiled threat to take those assets if they were not offered freely. So we care mostly about income inequality within a nation that is correlated with existing political coalitions, since we can threaten to use coalition politics to transfer income within a nation between such groups.
In effect, Robin is making a cunning observation that the reason why people are trying to "reduce inequality" might have less to do with naive humanitarianism - which is compassion not linked to common sense - and might have more to do with veiled self-interest; with benefiting themselves - with the law of the strongest.

Some people (here's one) are certainly naive humanitarianists in that they support income redistribution even when they themselves suffer from it.

The proper response to that seems to be education - at an early enough age. If only we can educate these people about the evils of compassion not backed by strong responsibility, they could learn that it is imprudent to support policies that give without requiring a return.

But such people do not represent the majority of voters. It actually seems plausible that the majority of voters - those who benefit in the short run from income redistribution - are far more cunning, and support it for entirely selfish reasons.

These people, too, might be convinced to an extent, but in this case education can only focus on the strong long term benefits of not stealing from the future. Then, even if we convince them not to steal from that which should have been used for investment - i.e. not to tax people's income; even if they hear that message perfectly, we will not be able to make them support dismantling their pensions, social security programmes, and other aspects of big government.

At best, we can convince them to steal less damagingly. By convincing them to support a sales tax instead of an income tax, we might possibly succeed in making them steal from that which would otherwise be consumed, rather than from that which would otherwise be invested.

But this is the theoretical maximum we can expect. As long as we have democracies where every vote counts equally, the majority will not stop taking from the successful minority, because it makes no sense for them to stop. They are in the majority. The successful are in the minority. It is the law of the strongest.