That's called a regressive tax system.
By definition, the tax system in the post you replied to is not a regressive tax system.
Poor people derive overwhelmingly more value from dollar $10,001 than rich folks do from dollar $1,000,001. (This is not controversial.) Thus, rich folks can--and should because they derive more value from the structures of the society that enables them to be successful and not hit over the head for their paycheck--pay progressively more to sustain that society. (This is also not controversial in reality, even amongst relatively right-wing economists.)
(Note: I do understand about utility, and how/why progressive tax systems help society. My only bone of contention here is that you're trying to redefine a specific term to have a different meaning.)
And then everyone starts arguing about how progressive the system should be to do that properly. :-)
I'm suggesting that we take substantially more from the ultra wealthy; many of whom already pay <15% tax. I'm also suggesting we tax the middle class less as well (who often pay more by percentage >15%) and the poor don't pay taxes until after they make a "live-able wage", i.e. only after they can afford food and shelter do we tax.
A flat 20% tax rate, plus removing loop-holes or tax refunds would dramatically impact the wealthy and middle class. Then we drop taxing the poor (which the U.S. already does).
I think it's naive to think we should just "raise taxes" to disproportionately take from the people who have money. They may have earned it, I don't want to take their wage, any more than I want to take from someone who works in the field all day.
That isn't to say that regressivity is a fatal flaw — tobacco taxes and other "sin taxes" are all regressive, but they're seen as good because the goal is to discourage behavior, not raise revenue.