Now, I don't have a problem with a film about the experiences of American soldiers in Iraq and I don't have a problem with a film that sympathizes with these soldiers either. What I do object to is the linking between 9/11 and the Iraqi invasion; the portrayal of injured and traumatized American soldiers as primary victims of the war rather than as aggressors; the portrayal of American deaths as painful and traumatizing while Iraqi deaths are shown to be clean and painless; and the general way in which Kyle is glorified as an infallible, morally superior superhero, the like of which just don't exist in real life.
This I mostly agree with, although I don't understand why you think the Iraqi deaths are shown to be clean and painless. They're certainly not shown as three dimensional in any capacity, but the drill killer scene, while not emotionally complex, is anything but. The film does not challenge Kyle's beliefs enough. From the midpoint onward, it seems like half the soldiers he encounters as the ones who tell him "This war is awful" or soldiers who have been disabled during combat, but at no point does anybody attempt to challenge his unfailing belief in his country or his country's intentions in invading Iraq, and that's why we're not talking about a great or even truly good film.
So, I don't believe this is a film that actively supports the Invasion of Iraq. It just doesn't denounce it like I would like. It's more interested in supporting our troops and how we need to bring them home, and honestly I'm fine with that once in a while. American Sniper gets partial credit in my book.