I too finally got a chance to watch American Sniper and although there were certain aspects of it that could have been construed as American propaganda, I don't think that was the film maker's overall intention. I definitely would not say that the movie was controversial in any way and while I did think that it was a good movie, it should not by any means be categorized as the best movie of the year. I think that Clint Eastwood did a great job directing the film and Bradley Cooper was phenomenal in the lead role but I did have some gripes about the movie.
First off, while I agree with Elias's point about fanaticism in both the Islamic terrorists and the Americans, the movie subtly references both the Christian and Islamic religions with the latter being touted as the malevolent religion. Several times throughout the movie does the character of Chris Kyle make references to the Christian God in his attempts to rationalize his actions during the war. The opposing viewpoint however is rarely mentioned. The only time the Islamic religion was when Bradley Cooper's character feigned ignorance over the Quran. Personally, I think that religion in general, especially a fanatical belief in any God is detrimental to society. I mean, all anyone has to do is flip through a history book to see that, but most Americans are blinded by what the media spews at them.
The second point of contention that I had with the film was this underlying notion that to be an honorable solider, one mustn't have doubts serving in a war or about war in general. I can't really delve more into this because I'd be spoiling an important part of the movie but it really irked me that in a country where people are allowed to express freely their beliefs and congregate to protest their government, are you really not allowed to question war? Especially if you are serving in the armed forces in times of war? I don't know how I feel about that notion.
Aside from those two issues I had with the movie, I do recommend that you watch it. It really does show how messed up war can be and the psychological toll it takes on soldiers.
I think the things you take issue with are more related to the fact that this isn't Clint Eastwood making a movie about Chris Kyle, its Clint Eastwood bringing Chris Kyle's autobiography to film. So to your first point, you're not going to get both sides of the story, and to your second point, that was Kyle's opinion - I haven't read the book, but I understand that is an accurate depiction of how Kyle felt. Supposedly the movie stayed pretty true to Kyle's overall attitude and thoughts, Taya Kyle said Cooper and Eastwood nailed the essence of Chris and the situation, though
MINOR SPOILER ALERT
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they did make up the hunt for the Syrian sniper (he was real, Kyle knew of him but wasn't involved in the hunting or killing of the guy). Typical Hollywood wanting a thread to weave through the story,as if we would need something more to believe he would want to go back, or we would miss the other common thread,the psychological toll it was taking on everyone in the family, and the irony of how he climbed out of that vs. how he died. The scene where he sees his brother on the tarmac was also not in the book, though I imagine Jeff Kyle must have felt that way, and maybe talked with Chris about it, or I can't see that getting in.
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Also wanted to point out that Chris Kyle and all soldiers are trained, consciously and subconsciously, to speak of the enemy as savages, to think of them as bad guys and less than human. I read an article that talked about how in WW2, when a soldier had a confirmed enemy lined up and ready to pull the trigger, they fired only 20% of the time. The US Military set about to improve this, to make the time between "aim" and "fire" an automatic, conditioned response. This dehumanization of the enemy was the main tool they employed - having them use words like savages, bad guys, animals, the constant chants using those terms and talking about the way they live in terms that equate it with savages and animals, etc. Firing rate was 55% in Korea, 95% in Vietnam - and mind you, in WW2 they were generally uniformed military, so there was little doubt, whereas Vietnam was more like what they're facing today.