Lane Kenworthy says people should tell the full story about tax progressivity. What has been presented attempts to defend the wealthy against the charge that they don't pay their fair share, but "it doesn’t make much sense":
How Progressive Are Our Taxes?, Consider the Evidence: Steven Dubner has a post on the “Freakonomics” blog titled “The next time someone tells you that taxes are not progressive…” He relays information from a new Congressional Budget Office (CBO) report, via Greg Mankiw, which lists effective federal tax rates for households at various points in the income distribution. The rates are higher for those with larger incomes. The implication is that our tax system is quite progressive.
But it doesn’t make much sense to look only at federal taxes. State and local taxes account for about a third of total tax revenues, and they tend to be less progressive than federal taxes.
If we take into account all taxes — federal, state, and local — the effective tax rate for the well-to-do is only a bit higher than for the poor. Here is one way to see this, based on data from the CBO and the Tax Foundation.