US citizens who earn their money outside the US get a tax exemption of US$80K on their income. Everything above that, they pay income tax on. They still have to file their tax form and claim the $80K as income, but they can deduct it from their total income to shelter it from taxes. The logic has many aspects: overseas workers are usually working in a capacity that increases trade with the US, also overseas workers are not able to take a lot of deductions that people in the US are.
If people live overseas and don't file their returns, they can be hammered pretty hard when they go home if the IRS audits them. There is a stiff penalty for not filing, even if you don't owe any money.
Besides, the US tax laws are so complex that the IRS can
find a way that you owe money. I'm pretty convinced that there is not 'right' way to file your taxes...you just have to show that you attempted to be as honest as you are capable of being.