Most commenters here seem to have a false impression of the distribution of taxation. "The rich pay little taxes" is disinfo. The truth is more like "the rich pay most of the taxes." The US has had progressive taxation since 1913. Today, taxes on the top 1% of earners comprise 40% of federal income tax revenue, top 5% comprise 60%, while the bottom 50% comprise 2% (however note income taxes are only half of federal r…
By itself, this doesn't really mean much; it certainly doesn't address "fairness". For example, even in an inverted regressive tax system, the rich could still pay the most in taxes. This is simply because they earn the most money. And the larger the ratio between rich and poor, the easier it is for the rich to pay the most in taxes, yet still not be affected as substantially by taxation.
Take an extreme example to illustrate: there are 9 earners making $100 per year and 1 earner making $10,000 per year. If the tax rate were 90% for the low-earners and 10% for the high-earner, the high-earner would still pay the most in taxes (more than 50% of total revenue), but few would call this system "fair".