The Iraq War was pushed by a group calling themselves neoconservatives. They were itching for a war regardless of the WMDs.
Its genesis was at least the mid 1990s per: https://en.wikipedia.org/wiki/A_Clean_Break:_A_New_Strategy_...
And then this group got more power under Bush's term and 9/11 happened and they responded by pushing for the Iraq war and got it:
https://carnegieendowment.org/research/2003/03/origins-of-re...
https://www.foreignaffairs.com/iraq/what-neocons-got-wrong
The WMDs were a convenient cause belli for the masses, but it was not the motivator for the war. This is why no matter how much doubt was created about the WMDs before the war, and there was tons and tons, there was no stopping it.