[mpreda]

A flat consumption tax would be regressive if the two extremes (rich vs. poor) would buy the same goods; but they don't. The very poor buy cheap food, the very rich buy diamonds and services ("dog walking", "garden design", "personal trainer"). Not to mention the two buying different kinds of habitation, in different locations, at very different price-points.

[stanleydrew]

This is all true but doesn't invalidate the point unless the rich and poor are spending the same proportion of wealth/income on these various categories.

The fact that the rich can afford to save more of their income proves that isn't true.

A more pedestrian proof would be that even if I make 10 times as much money as someone else, the most expensive gallon of milk I can buy is still only double or triple what a poor person would pay.