There's nothing inherently evil about progressive tax rates, except that they create an inherently more complex tax system than a flat tax would be. Complexity creates all sorts of ill effects, from tax avoidance to inefficencies to an inability to predict outcomes to tax-motivated investments and beyond. It is a very serious flaw, and I personally would dump our current system for a flat tax.
Clearly a 20% flat tax on all income -- which, BTW, would include such things as the proceeds of life insurance, the accretion in value of stocks and bonds, etc., none of which we have ever taxed in this country -- would be worse for us all than a progressive tax that ran from 0 to 15%.
So, why do so many like the flat tax? Why do some tax pundits oppose it?
A flat tax cannot be dodged. Whatever the result is of one equation, multiply your income times the rate and that's what you owe. Do up your return on a postcard and mail in what you owe. No more lobbyists, very little IRS. Easey-peasy.
But a flat tax also distributes the weight of the total tax burden in a way that none of our progressive tax rates ever have, shifting a sizable portion of that burden down from the wealthiest taxpayer onto the middle class and working poor. This defect cannot be cured; once you create a different tax rate for anyone, that tax is no longer "flat". Once it is no longer flat, it is open to the same complexity defects as our existing progressive tax rates.
Additionally, as I am sure has already been mentioned, many tax pundits and economists feel that our economy will suffer if capital gains (gains from the sale of assets, such as stocks and bonds) is not taxed at a lower rate than ordinary income (wages, stock dividends, etc.). This is because investment in assets is the engine of our economy; it creates factories as well as the credit to borrow to build them, and if that dries up, we'll all be sunk.
With a progressive tax, you can have various schedules for capital gains v. ordinary income. However, with a flat tax you can't as, once again, any alteration in the rate schedule will mean the tax is no longer flat.
Most pundits (last I looked) think we'd need a flat tax rate of about 14% to generate the revenue that our existing personal and corporate income tax generates. There's serious concern that this would be highly detrimental to our economy as too heavy a hand on capital gains, and serious concern that it would be too heavy a burden on mid-range taxpayers.
Then of course, there's the agony of changing our tax system to such a dramatic degree -- there'd be loss and waste and inefficiencies, so there's debate about whether the candle is worth the game.