Progressive tax means that richer you are, higher marginal tax rate you pay. So, the average tax rate for a rich person is designed to be higher than a poor person.
The "unfairness" argument usually goes like this: "everyone is born equal in this nation and everyone should pay the same tax rate regardless his own money-making ability."
I am sorry, my friend, this is total horse-shit.
First, let's see where the tax money goes once it's collected from you and me. The single largest expenditure is National Defense (including Veterans Affairs). It's over $700bn and over 25% of the total budget.
Then, you tell me who benefit more from National Defense, me or Warren Buffet? For me, there are not much to be defended with. Let's say if Cuba invades US, I don't get much to lose. Well, that can't be true for Warren Buffet. He has the most stake in US and he will be the biggest loser if anything happens.
Since rich people benefit more from programs like National Defense, it makes perfect sense that they pay more.
People are dying to protect the country. Well, those poor people, to be precise. So, in order to maintain a steady stream of fresh bodies for the army, rich people have to support poor families. Therefore, Health and Human Services (the 2nd largest item on the budget) makes perfect sense.
Even small items on the budget, like those national highways, rich people drive more and benefit more. Poor folks sometimes don't even have cars! Why should they pay for something that they don't even use?
Education, another example, why should poor people pay for it given the fact that they have the higest drop out rate and lowest admission rate to college?
NASA, haha, do you think people in Harlem give a rat ass about what happens on Mars?
Oh, the Justice Department, the cops! You don't even want me to go there.
This list can go on and on.
The fact is "rich people, who may not even realize it themselves, benefit more in this country by government spending." Of course they have to pay more. This is only FAIR to do so.
Ok, now you may say why progressive tax? Rich people are paying more tax even if their marginal tax rate is the same as poor people.
Here is why: the margin utility of each extra dollar is decreasing and it's utility maximization for the society by taxing higher marginal tax rate.
Let's assume you only earn $1000 a month. This $1000 means a lot to you. It pays your rent, food, and other necessities.
But for others, Bill Gates for example, any extra $1000 means nothing to him. He can even give away the money to support aerospace programs. Well, some millionaires are exactly doing that.
So, if I, as the government, have to tax some money to support the programs I just mentioned earlier, I rather take the money from Bill Gates than from you. Consequently the marginal tax for rich people is indeed progressive. The more money a person makes, the additional dollar will be taxed more as it means less to that person. This tax rule minimizes the impact on the society as whole due to taxation.
Unfortunately, some people has a different utility curve when it comes to money. They will cry out loud whenever you take his money away even though they have little to no need for that money. We call them money-hungry self-centered cheap-asses. Or in short, Republicans.