Logic is not the problem, differing assumptions are the problem.
It seems you assume the Iraqi people want to be liberated by an infidel nation.
It is easy to assume all the people in the world share our values and aspirations. Sadly, that is not always the case.
Have you considered the question, what if the Iraqi people do not want liberation from a nation their religion labels as infidel?
Iraq is a threat to the U.S. and their ability to threaten the U.S. must be removed, that's the mission. Getting too caught up in the rhetoric would be a mistake, imo.
All Muslims are not the same, any more than all Christians are the same. Ever hear of the "religious wars" in Europe? To the Catholics, Protestants were "heathens" and heretics, and to the Protestants, the Catholics were.
El Cid allied with Moors who were loyal to the King of Spain to drive out other Moors from Spain in the 1400s. There are countless examples.
YOU expected giant crowds of people with banners and American flags---but these people were betrayed in the 1990s. They won't forget that betrayal, but, equally important, they won't ignore the fact that WE ARE THERE TO HELP THEM NOW! They will cheer us, and sooner, rather than later.