If one considers the principle of marginal utility, the higher nominal rates of a progressive tax scheme take from the wealthy only those dollars that have less marginal value. A so-called 1flat tax is therefore really a nominal flat tax; in real terms, a flat tax is actually regressive. To illustrate, consider the effect of taxing at ten percent the first and last one hundred dollars earned by someone with a million dollar income. The ten percent taxed on the first hundred dollars of earnings takes money that, in the absence of a high income, would be essential for mere survival and thus has high value. The tax on the last hundred dollars might force the earner to, for example, opt for the silver shift knob rather than the gold shift knob in his ferrari. Still a taking, but the value of the shift knob downgrade obviously pales in comparison to survival needs.
Thus, a flat tax is flat in nominal terms only. In terms of real value, it is actually regressive. A so-called progressive tax, depending upon the steepness of the progression, may in fact not be progressive at all in real terms, but serve only to restore some semblance of flatness. A carefully structured "progressive" tax is therefore inherently more fair if one is attempting to reify egalitarian principles in a tax code.
I accept the idea of spreading the wealth in order to make the odds better for all not just the rich. I believe the rich can afford more and therefore should pay more in taxes and the poor need all the help they can get with the way things are today,
Equality means treating everyone the same. Equality requires equal treatment no matter whether a person makes a lot of money or very little. Equality should not differentiate between income, race, religion, age, ethnicity, sexual orientation, or other similar categories. But a progressive tax does just that by requiring people with higher incomes to pay a larger percentage of their income as taxes.