The "weapons of mass destruction" was kind of used as a pretext because they didn't believe such an argument would win popular support. It's somewhat abstract and rooted in a kind of ideology rather than pragmatism. They also genuinely believed that Saddam did have weapons of mass destructions, but just couldn't prove it. They would be found after invasion. Just a little white lie in the meanwhile.
That's really all there's to it. People get all cynical about "freedom and democracy", but that really was the goal, as a kind of "enlightened self-interest". After 9/11 this only became more acute: with the middle east part of the liberal hegemony, there would be no more Al-Qaeda (or they would be severely weakened).
Because they lied about the pretext, there was little to no broad discussion about any of this so they just operated in their ideological echo chamber. There was no one to really point out this entire notion was perhaps well-intentioned but also rather misguided and ignorant (to say nothing of the execution, which was profoundly misguided and ignorant).
The Iraq invasion was wrong, but the occupation was worse.
But yes, I broadly agree with you. Although I'm somewhat sceptical you can do this kind of state-building imposed from the outside in the first place though. But if you must do it, then the way the US went about it was clearly the wrong way.
Are you sure you explained the thought process, or you just explained the justifications and the propaganda in support for a plan that had different purposes? Because of course if you need to convince an entire country (including its politicians and intelligentsia) to start a war, handwaving things such as "democracy", "domino effect" and spreading fears about WMDs is an obvious strategy.
Turns out, if you come in with guns and start making demands the people will hate you. And you need the people. The people aren't just the dudes living in a country - they are the country.