Personally I like a flat tax because it drastically simplifies the tax system and removes the loop holes that wealthy people who can afford accountants use to achieve the lower effective tax rate stated in the root comment. It also deletes the tax prep Industry and a significant majority of the IRS, these Ultimately act as drag in our economy for arguably a net negative benefit.
A flat tax isn't fair unless every other form of expense was flat as well. Which means rent would have to be some percent of your income and the same for power, healthcare and so forth.
The tax progression is pretty much the simplest part of any tax code anywhere in the world already, so targeting that as the thing to simplify is either stupid or hypocritical.
The loopholes and complexity lies in the fact that, in order to account for people who are self-employed, you typically want to allow subtracting certain kinds of expenses from people's incomes for the purpose of tax computations. That's where the mess starts because then people start playing games with how those expenses are classified and structured, and wealthier people can afford to employ expert players of those games, making the whole game unfair from the very beginning. That in itself should be justification for a progressive tax code.
It'd be awesome if we could remove those subtractions from the tax code, because that would be the way to really simplify things. Unfortunately, it's also a really bad idea because it would severely punish low-margin activities, and from a societal point of view, we actually want most economic activity to be low-margin (because that provides the highest value to the end-user/consumer).
So we're stuck in a world where we'd like to simplify the tax code, but doing so requires diving deep into the nitty-gritty details of how it all works. And for people who have that knowledge, it's more profitable to play the game by selling their knowledge to the aforementioned rich people so most of them end up doing that instead of taking up the thankless political work of actually simplifying things. At least, that's how the incentives are playing out today.