Iran was actively supporting the Shiite movement and the US government liked Saddam Hussein, even after kicking his ass out of Kuwait. By encouraging the rebellion and then allowing it to be crushed, they pushed back Iranian influence, strengthened Saddam Hussein, and had all the justification they'd ever need to implement sanctions and thus further terrorize the Iraqi population. It was never about helping Iraq as a country.
At least that is the only logic I could think of for doing something so intuitively stupid.