I went to a minor national park over the summer (Abraham Lincoln Birthplace National Historical Park) and there was a map of the United States showing all the national parks in the country with a "Gulf of America" sticker placed over "Gulf of Mexico".
"Milton, 42, and his wife donated more than $1.8 million to a Trump re-election campaign fund less than a month before the November election, according to the Federal Election Commission."
There were a few reasons but an important one is that Cheney, Wolfowitz, and Rumsfeld were convinced by Laurie Mylroie that Iraq really had something to do with 9/11 and everybody in the administration was paranoid about another attack. Wolfowitz also felt guilty about the George H. W. Bush administration abandoning the Shiites. All of them (except maybe Powell and Armitage) already disliked Iraq, felt like the first war was unfinished business, and didn't need much prodding to go after Saddam but the 9/11 connection they thought existed gave it urgency. Ultimately it came down to Bush and he probably thought it sounded like a good idea and not for any particular reason.
Cheney and Rumsfeld had a history of paranoid fantasies going back to their Team B fake "missile gap" work in the 70s.
Both of them knew how to work the DC machine, but neither of them were ever bothered by little things like "facts". I don't think we'll ever know what they really believed.