It's shortsighted thinking like that that leads to big problems. Yes the rich pay the large majority of income taxes, because they make the large majority of the money. That's really not shocking. Under any form of an income tax they'll spend the most because they earn the most.
What the problem is that as jpx pointed out the current tax system greatly benefits the very rich. When I say very rich mind you I'm not talking about you or AA who make good incomes but people who make way more than the top 1%. While the republicans have successfully conned you into thinking this is a war on people who've earned their money, they don't talk about the other tax benefits that come with being rich.
Here's a figure based on the quintiles and what they pay in payroll and excise taxes as a part of their income in 2007
The same regressive trend exists on state levels as well
The idea of the "burdened" tax payer does exist, but it's not the wealthy.
One more graph just for fun, this is the total tax bill federal and state broken into quintiles but expanded upon in the top 90%.
There's a stiff rise as you make money up til the highest quintile. The highest quintile starts at about 100K. Basically meaning that until you earn over 100K you're paying out the nose the more you earn. When you hit the 80th percentile things start to slowly go up, not at the stark increase you see when you first look at the graph.
There's barely an increase going from 90-95 to the 95-99 then a drop off for the top 1%. Basically the top 10% garners a more favorable take
More food for though, from 2000-2009 the effective tax rates of folks earning 200K+ adjusted gross income as part of their group.
37.2% had an effective tax rate of 15-20%, 30.5 20-25, 16.7 25-30 and 10 at 10-15. Basically the rich pay more in taxes that is true, but it's not by some astronomical account when you factor in their income.
I think the american tax code is very backwards and while the income tax is progressive to a point, it's the only tax that is, the capital gains is regressive, retirement taxes are regressive, and so on so forth.
Basically the rich have us by the balls, you can choose to embrace that I choose to feel disgusted by it.