the thing i still don't understand at all is why they thought they would be able to do it successfully. i mean i get why they believed so strongly that it was important to change the government in iraq, but why they believed they had the ability to do it is still hard to understand, partly given the benefit of hindsight but mostly given that presumably they should have expected to face the insurgency that they did. the 90s and 00s really do seem to have had a pretty different structure of feeling, mood, belief in a certain kind of possibility in the west. i suppose one answer is that they didn't really care if iraq ended up in fragments as long as they were able to reshape the middle east and access to energy resources along with it, but i've never found that convincing.
it's both an interesting and important question that I feel like I can take a stab at, at least in a historical sense
tldr: hubris and ignorance
I think the basic answer isn't that the neocon clique didn't care - it's that they legitimately thought they would go in and topple Saddam and Iraqis would be so happy and grateful that they'd turn into ersatz Americans complete with a functioning liberal democracy and the Iraqi equivalent of mom (presumably just mom), apple pie and baseball. the planners and executors of the Vietnam War had essentially the same delusion. in both cases that democracy-building was a side effect of the main geopolitical goal - respectively, containing communism and reshaping ME/access to energy resources - but still an important secondary casus belli, if only for the way that Americans need to see themselves. the Romans had a silly and elaborate ritual for basically pretending to openly declare war against an enemy without actually telling the enemy - in their case it was to do with ensuring divine justification, but they're about concocting a narrative by which you tell yourself that you're on the right side, that your goals are not merely to conquer and take.
you'd think Vietnam would've cured American policymakers of this delusion, that everyone wants our way of life if only given the opportunity. especially people like Cheney and Rumsfeld, who saw that policymaking and its failures up close as rising natsec apparatchiks. clearly it didn't, so the question becomes, why not? one big reason is a different delusion, that of post-Cold War Pax Americana, the lone superpower, fed by a string of relatively low-cost and "successful" interventions - Panama, Haiti, and of crucially/of course, Iraq I. even failures like Somalia were on too small a scale to disrupt the narrative. this is what you're talking with different "belief in a certain kind of possibility". at the same time you have the conspicuous failure to intervene in Rwanda, which reinforces the argument for "humanitarian" intervention.
another reason that I'm less sure about but suspect and would make sense is lack of true area expertise in the State Dept, another similarity to Vietnam. in that case essentially every area expert on East and Southeast Asia had been purged for reporting honestly on conditions in late 40s China (i.e. the "who lost China?" nonsense) combined with early McCarthyism, people like John Paton Davies, John Fairbank etc, so that when JFK et al were considering war there was no infrastructure of expert knowledge to inform their decisions. you can't just create something like that out of thin air, it takes years of people getting that expertise through graduate training and hands-on experience. in the case of Iraq, American natsec, geared toward USSR etc for so long, only really started focusing on the ME after 9/11. two years isn't nearly long enough. the necons were ill-informed and arrogant enough to not understand their own ignorance.
lastly, the insane, catastrophic decision to impose hardline de-Baathification, the impact of which cannot be overstated. it more or less destroyed any chance of post-invasion Iraq becoming a functional, stable society. my understanding is that was essentially a rogue decision by Wolfowitz, Bremer, etc under the guidance of Rumsfeld - exact responsibility being hard to determine bc everyone hardcore CYA'd as soon as it become clear what an incredibly stupid idea it was, but in any event they didn't consult at all with intelligence or other security people. the fact that they did that will never not blow my mind.
that's my 0.02 anyway. there are other reasons I'm sure but I don't think that's a bad general picture.