A progressive tax means that the less you earn, the less you pay, or that there is a built in advantage that taxes poor people less. The income tax system as it is now run is a progressive tax (at least, on paper). The top tax bracket now is 38% of income for the richest Americans, although almost no one pays that amount.
A sales tax, on the other hand, is regressive, because everyone pays the same percentage tax, even if they make much less money.
The main argument against progressive taxation is that it is a penalty for being successful. So if you have built a business and worked hard and earned a fortune, then you pay more money as a result, so where is the incentive to do well? That doesn't seem to stop people from pursuing and achieving wealth, but some would say a progressive tax discourages investment as there is less money to make in America before higher taxes kick in.
To me, the major argument against progressive taxation is this -- why should a person who does better (is able for whatever reason to earn more money) be penalized for that? Is it not more fair to tax everyone at the same rate?
In a progressive tax system, people are taxed more based on their ability to pay than on anything else. The government is saying "you've got plenty of money so it's okay to take a higher percentage from you than from someone else." That does not necessarily make sense. It seems that everyone should pay the same percentage of their income because then everyone would be treated equally.
Under a progressive system, taxpayers are not treated equally. The better-off are penalized for making more money. That, you can argue, is not fair.
Here's a link that makes this point.
The practice of progressive taxation is applied primarily to income tax. This means that higher a person earns, higher the percentage of income to be paid as tax. Thus the with rise in income the increase in tax is more than proportional. There is only one argument to support the view that progressive tax is unfair. This argument is that it discriminates against the persons with higher income. This discrimination can be made to appear worse to those who believe that the higher income of people is direct result of the higher efforts put in by them.
It should be noted that there are many arguments against imposition of progressive tax other than being unfair. These other arguments oppose progressive taxation on the rounds that these are likely to hurt the overall interest of an economy rather than help it.