Within hours of the planes hitting the towers on 9/11, before any information was in, Rumsfeld's aides were drawing up plans for striking Iraq, despite zero evidence linking Saddam Hussein to the attacks. The number one priority for the White House, above finding out who the real culprits were, was to figure out how to use it as a rationale to invade Iraq. This is not really a controversial viewpoint, it is documented fact [1].
When the 9/11 rationale for invading Iraq became untenable, it was replaced by the idea that Saddam had Weapons of Mass Destruction, that he'd definitely been procuring uranium from Niger. Except these were lies too (and the WH knew it, because they'd sent Joe Wilson to investigate and he'd reported back as such). When Wilson heard them saying it despite knowing it was false, he contradicted them in public [2]. In an act of retribution, the WH leaked his wife's position as a CIA agent, burning valuable contacts and networks, and endangering friendly lives.
Then they moved onto the argument that regardless of WMDs, the Iraqi people actually wanted the invasion anyway, US forces would be welcomed as liberators by gift-bearing citizens, etc. When that didn't pan out either, a final argument became that Saddam was a tyrant and that fact alone provided sufficient moral and legal justification for preemptive war (i.e. The Bush Doctrine) [3].
[1] https://www.cbsnews.com/news/plans-for-iraq-attack-began-on-...
[2] https://www.bbc.com/news/world-us-canada-49856792
[3] https://www.pbs.org/wgbh/pages/frontline/shows/truth/why/