There method is more progressive and they have been proud that the poorer end do not contribute much
Except that poor people tend to mostly get their money from wages, and rich people don't
Different treatment of different sorts or money result in a billionaire paying a low percentage than his secretary.
Something similar can happen here, with generous treatment of the rich, for example as "carried interest" and capital gains.
You have perhaps heard of super-rich, multi-billionaire Warren Buffet.
Warren Buffett and His Secretary on Their Tax Rates
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"Buffett's secretary since 1993, Debbie Bosanek, sat next to her boss just hours after being invited by the president to the State of the Union address, where the president made her the face of tax inequality in America.
Bosanek pays a tax rate of 35.8 percent of income, while Buffett pays a rate at 17.4 percent.
"I just feel like an average citizen. I represent the average citizen who needs a voice," said Bosanek. "Everybody in our office is paying a higher tax rate than Warren."