Try doing what the rich do to pay zero tax and you end up in jail.
Not true. If you work for a paycheck, and receive a W-2, you are screwed. But if you run your own business, or work as a contractor, most taxes are avoidable even for a "little guy."
I pay very little tax. My income is above the median, but I don't think many people would consider me rich. I own three domestic corporations (a Delaware C-corp, a California S-corp, and a Nevada S-corp), and an overseas Cayman Islands corporation. These cost just a few hundred bucks each to set up. Any middle class person could afford to do the same. I can report income through whichever jurisdiction and type of corp offers the best deductions for that particular type of income. I can move income between corps by selling "services" or paying license fees. I avoid paying personal taxes by living off non-taxable loans, rather than taxable income, from the corporations.
All of this is perfectly legal. I was audited by the IRS once, and had to pay a fine of $420 for a bookkeeping error, but otherwise they said everything was fine.
Of course these loopholes were set up for the rich, but there is nothing to stop the rest of us from using them too. If you think about it, we have a good system: people that don't mind paying taxes pay them, and those of us that prefer not to, don't.