Laws. There are a lot of exceptions in IRS law that they can take advantage of.
Also a lot of wealthy people don't have their wealth in piggy banks like Scrooge McDuck that can be readily access, there money is in company assets and stocks. There are a lot of exceptions in the IRS for business purposes that they can rely on. At the same time, as a result of them not paying taxes, it should allow for capital spending to grow companies and create jobs (hence the reasoning for these exceptions).
The IRS gives these exceptions to protect businesses and therefore the economy/jobs. Rich people have their assets in these companies and can therefore take advantage.
There is also double taxation defenses because in theory, a wealthy stock holder can get taxed on their own gains by the IRS as well as via Corporate Taxation. (Basically their business gets taxed and then they get taxed).
Sales/Property Tax is actually a far more efficient means of taxation but it is also just as ruthless to the poor as the rich.