Levels of wealth are something that is affected by diminishing returns. That is, one dollar (the marginal dollar) for a rich man serves far less of a purpose than the marginal dollar of a poor man. This is the basic justification of progressive tax. A flat tax would, overall, remove more utility than a progressive tax would for the same amount of tax income.
The main issue with progressive taxation in the United States is money lost through tax loop holes. A progressive tax system generally has a number of ways to reduce tax liability. When tax liability is reduced, the actual amount of taxes that would of normally been collected is greatly reduced. A flat tax system, such as in the Russian Federation has very few write offs and the full amount in taxes is easily collected.