You are messing causes and effects. Inequality itself is not nearly as bad thing as many people claim it is.

Let's take an example. Two individuals are in the same position, have same amount of wealth and income. One of them decides to change his job to a better paying and also does some extra hours. Another one also decides to quit his job, but he moves to a tiny house and will make only every now and then little money by selling some organic vegetables.

Inequality increased but how that was a bad thing? Both individuals did it because they wanted to do that.

Usually the bad things that are associated with inequality are not caused by inequality itself. Instead they are caused by other things that cause also inequality at the same time.

If, for example, inequality is caused by corruption, then it's pretty much useless to fight against it by redistributing wealth. Problem will still exist. But if the corruption is removed, inequality will also disappear because the cause has been disappeared.