You seem to have the same problem mixing things up as a lot of others, so don't feel like the Lone Ranger. It'll be a lot easier to understand if you separate the original reasons for invading from the reasons we've been there since the Hussein government fell. They're two completely separate things and should be treated as such.
If you're old enough to remember Iraq's invasion of Kuwait, the brutal suppression of the Shia in the south, and the use of chemical agents against the Kurds in the north, you can hardly argue that Hussein wasn't a problem. He intentionally gave the impression that he had WMD's and was developing more, so it's also not hard to see why the arguments over the urgency of the invasion were swayed by intelligence estimates that turned out to be wrong.
Since you remember the "mission accomplished" thing, you should also remember that the war really did end then, just as the Spanish-American War ended with Spain's defeat. And just as that led to the Philippine insurrection, we've subsequently dealt with insurgents in Iraq. Where Philippine autonomy was to be given them after forty years, we'd like to get out of Iraq somewhat quicker, but dare not leave abruptly for fear that would leave a Shia theocracy inimical to our interests in the middle east. Even if the Iraqi government eventually turns out not to be strongly pro-American, what we'd like to see is a secular government that respects all the major groups in Iraq: Shia, Sunni, and Kurd, and one that has democratic principles. That would, strategically, be a political wedge between Damascus and Tehran, and that would be good enough, though nobody in government can say so for diplomatic reasons.
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