The wealthy earn most of the money, frequently on the backs of the working class, so of course they pay most of the taxes.  
They have most (nearly all) of the money.
For those who want "fair" taxes, first ask for fair wages. 
What should the ratio be:  highest earner to lowest earner, maybe 3 to 1?
If that were the case, maybe a flat tax would work, maybe.  Otherwise, it's progressive taxation on income.