First of all, please note that a flat tax is not regressive. A flat tax takes the same percent of everyone's income. A regressive tax takes a higher percentage from poorer people.
There are said to be two major benefits of a flat tax. First, some see it as more fair. They would argue that there is no reason that rich people should have to pay a higher percentage of their income in tax. It would be more fair if everyone paid the same percentage. Second, it would be much simpler. People would have a much easier time filing their taxes if there were a simple flat tax.
People who oppose a flat tax argue that it is unfair to the poor and middle class. They argue that the rich have benefited most from our system of government and that they can afford to pay more taxes. Therefore, they say the rich should pay more in taxes to keep the system.