Excellent subject, and one answered by 4 letters: PNAC.
More on PNAC later, but a reassuring comment on every Iraq veteran in uniform - their service was brave, patriotic and, yes, noble. They all responded to their nation's call to duty, and many nations from all over the free world responded to that call. On the face of what the US told the world, the "just cause" was to prevent a rogue Saddam-led nation from developing WMD (since then, proved to be overstated), and to retaliate for its murderous support for Mideast suicide bomber terrorists and their survivors (true) and their increasing violence and mass murder of Its own dissenting and/or ethnically isolated populations (true in part). In addition, the Baath Parties of Iraq and Syria had squelched the functions of democratic governance and began governing like an oil-funded Mafia kleptocracy, and a bunch of Reagan/GHW Bush era "experts" & the prestigious Council on Foreign Relations convinced many patriotic leaders that a Jeffersonian democracy in Iraq would become the seed needed to combat totalitarianism across the Mideast and then elsewhere in the world.
What many who were called to serve were led to believe that was contrived by PNAC, and unwittingly by Bush Jr., however, was that Iraq was part of an evil "axis" of rogue nations that were behind the Islamist attacks committed by Al Qaeda. Still, the fact that this American-made falsehood was contrived, there was a partial truth to it - to PNAC and others who aspired to see a more democratic and pro-West world, Iraq, North Korea, and Iran were examples of unpredictable anti-Western irritants with a penchant for internal brutality. But there was no "axis" between them like there was in WW2 between Tojo, Hitler, & Mussolini.
Nonetheless every Coalition serviceman must be commended for faithfully completing a challenging overthrow of a dictatorship in short order, and then combatting a grassroots insurgency that the Coalition's leaders had not anticipated nor planned for. And through it all, even though the Iraq War failed miserably at reducing Islamism and its terrorist components (instead it became a proving ground for grassroots terrorist tactics), it did depose a dictator and created a partially Western-aligned, partially functioning democratically inclined constitutional government in the center of the Mideast's -------------- Oil Patch, and it helped a bunch of targeted ethnic minorities survive and become represented in Iraq.
So, Iraq War vets, stay proud of your service to righteousness. Though the war itself was conflated Saddam with Al Qaeda (the Baathists and ------ generally despised Bin Laden and Al Qaeda and the Taliban), and though some commands required mission safety protocols, nearly every single Coalition service person and those supporting the Coalition's efforts did their duty with righteous intentions.
In "Just War" theory, the highest levels of US government contrived a war that they believed would lead to noble outcomes and that would show that dictatorships could be overthrown and that the world could become safer for democracy. Was that "unjust". Is it fo us to judge?
Btw, for more background on PNAC, see: www.mit.edu