Did we ever figure out why the Bush administration was so gung-ho about having a war with two countries? Did we ever figure out why we invaded Iraq?
Basically the Bush Administration was made up predominantly of people who'd been wanting to invade Iraq for a decade and were looking for an excuse. Give a gander at the Wikipedia entry for
Project for a New American Century.
Notably, a paper signed by Wolfowitz (among others) urged Bill Clinton to invade Iraq as a bulwark to promote democracy in the Middle East -- basically, the neocons were trying to provoke an Arab Spring. Damningly, the report noted that the American people would be resistant to such a plan and it would take an event along the lines of a Pearl Harbor to get them to agree to the plan.
(Conspiracy theorists, of course, use that to promote "9/11 was an inside job" whackjoberry. I make no such claims; I merely suggest that the neocons were ready to capitalize on a tragedy if one were to happen.)
Bush was swept up in all of this, plus he had his own personal reasons for wanting to take Saddam out.
Essentially, the plan to go to Iraq was underway long before 9/11; once 9/11 happened, the administration scrambled to find any justification they could for the already-decided policy, and seized on any flimsy evidence that Iraq posed any kind of threat while ignoring the overwhelming evidence that it didn't.
Ultimately, if Iraq -- or any other Middle-Eastern nation -- flourishes as a stable democracy, the neocons will claim credit, and if it doesn't, they'll blame Obama.
(And it should probably go without saying, but the Arab Spring has fuck-all to do with our invasion of Iraq, though the neocons will be happy to claim credit if it ends up the way they want it to.)