The tax code has been manipulated over the years to favor the wealthiest in America. This was clearly demonstrated when it was revealed that Warren Buffet was paying a lower tax rate than his secretary. Buffet was paying around 15% while his secretary was paying around 30%. These deductions are mostly through capital gains. Nominally, the tax on the richest in America is 39.6%, but there are ways to get around this. In term of how much money American citizens are paying to the government the rich are paying more money. However, the effect of the loss of money is much greater for the middle class and the poor than it is for the very rich. Say a hedge fund manager is making $20 million a year and he gets taxed at 50% of that income. He will still end up with $10 million in retained earnings which is still a significant amount of money and will do very little to change his financial state which is very good. Now lets say we have a teacher that is making $40k a year and she also gets taxed at 50%. She only has $20k in retained earnings which is a significant drop because she already had a low salary to begin with. Now she can afford even less than what she could with $40k a year and her financial situation just got a lot worse. It is clear that the tax rates that everyone has to pay effect the wealthy much differently than they affect the middle class and the poor. Progressive taxation remedies these differences.
Supposing we had a flat tax, those with the highest incomes would pay the most money. After all, 30% of $300k is more than 30% of $100k. So even with a flat tax, the rich would pay more taxes than everybody else. But we have a graduated tax. The more income you have, the larger percentage of your money you have to pay in taxes. So the tax code is not geared in favor of the rich.
No, it favors the poor because the higher someone's income, the higher a percentage of tax they have to pay. For example, someone who makes 15K per year (could be considered "poor" by US standards for practical purposes) will pay less cents on each dollar they make than someone who makes 500K per year (could be considered "rich" by US standards for practical purposes) would have to pay on each dollar they make.
If the rich had to pay less cents per dollar they make then it would favor the rich.
If everyone had to pay the same cents per dollar they make then it would be equal.
As is now, the poor pay less cents per dollar they make so it favors the poor.