The problem is... this is not the problem.  This is a symptom.

The praeto principal says that 80% of the work is done by 20% of the individuals.  These 20% should be rewarded more then the average person.  Because we would like this group of people to continue working.

However, what most people point out as the rich, aren't really the rich.  Rich, by the tax codes are merely dual professional income families.
But, the ones we despise are those who take everyone's money by extortion.  Through govern-cement redistribution methods, or money printing methods.

Lets say you had a central bank.  And so, you can get money for free.  And then you lend it out at interest to someone for 2%.  That's free money.
And then that person lends it out at 4%.  That's free money.
That's free money that the people on the bottom do not have access to, but we pay all of that percentage.  The interest is not paid by people at the top, it is passed down, and everything / everywhere is laced with that fee.  If you rent, you are paying the landlords mortgage.  If you buy gasoline, you are paying the business loan.  Etc.