We are going to have to disagree on that. In my view, it is significantly more moral and effective for everyone to pay a fixed percentage of their income than for some to pay less than nothing and others to have nearly half their income taken. Also, if the government were not so large and powerful, we could pay for it with less taxes(another reason that Republicans push for tax cuts, they view the large federal government as problematic).
Flat percentage taxes are terrible; do some research into marginal utility and you'll see why. Now, I do agree that having a tax system where the "lowest income" folks effectively have negative taxes is not great - although it's complex in the US because even if you have negative income tax, does that offset sales taxes or property taxes hidden in rent? I don't know that I've ever seen that detail (and it also depends on location).
Most people that talk about "fair" taxes really mean "equitable" taxes, which doesn't help (just look at the name of the misguided proposal for US going to national sales tax called Fair Tax). The only "fair" tax is the same exact tax amount per person. The most "equitable" tax is the one that impacts each person the same which is what our progressive systems try to do that by having the tax rate be, well, progressive. However, I think an equitable tax is inherently impossible, because there is no way that even a progressive tax rate will affect two individuals with the same value of assets and income the same, because of differences like geography or any number of other factors. So, given that, a progressive tax rate based on nominal values is probably as best as we can do, but see my previous post for a system that I think is way better than either sales or income tax.
Afterthought: It's strange that taxes are based on income or wealth anyway. No other purchasable thing* is priced based on income: utility bills, food, and basically everything else you buy is priced independently of your income** - why are public programs (taxation) priced based on income? I guess this goes back to what a "fair" tax really is - it is the same price for everyone. And yes, I realize you'd have to figure out some alternative (like payment in kind maybe) if you have a portion of the population that does't have the currency for the fair tax.
* Public services funded by taxation are a type of "purchasable thing" even though they are kind of diffuse. The whole "I buy civilization with my taxes" idea (probably misquoted).
** Yes if you have higher income you might buy higher priced goods, or might buy more quantity of lower priced goods. But if you earn a million dollars a year, that doesn't mean you pay $300 for a gallon of gas instead of $3.