Their job...not ours
If the people of Iraq were so unhappy with Saddam, they should have taken him out without our help. Saddam was effectively defanged and neutered. He was no threat to his neighbors and completely unable to repeat the terrible acts he committed against his own people in the 1980's.
Its not our job to go about dethroning decrepit old dictators. George Bush based this war upon a false claim that Mr. Hussein was a threat to the American people. That simply wasn't true. The American people would have never tolerated going to war simple to take Saddam from power. That's why American public opinion is against the war today.