Watching the trailer again, I think it's possible to condense the reasons why I don't like it into two points.
1. The opening narration sounds like middle schooler emo prose, and is obnoxious on those grounds. If the game isn't being played completely straight, then the fact that it isn't might be lost on that audience.
2. The trailer seems to be deliberately (or maybe accidentally, it's a remote possibility) linking itself to all the mass shootings we see here in Freedomland and occasionally elsewhere, when I actually don't think the game is going to be about that, and could just be drawing a misleading connection for the sake of publicity and edginess.
There's another major one that some people also find offensive, but that doesn't affect me personally:
3. The violence depicted is graphic, sadistic, and personal enough that the game is genuinely disturbing, with no clear message or intelligence about it to justify it (unlike other games that try similar things, somewhat like Spec Ops: The Line).
Both 1 and 2 could be fixed if the trailer didn't have any narration, and was just that gameplay footage. All three will probably be more or less resolved when more information is released. To elaborate on 2, judging from the aesthetic and minor things like how people are just milling around outside the building the character starts in, I don't think the world this game is taking place in is supposed to be like reality. So while the first reaction of viewing the trailer is to link it to mass shootings, it doesn't seem like that's actually what the game will be about. Obviously it's still a game where you shoot lots of unarmed people, but reasons for doing so and the world that it's happening in are likely to be different enough that it's not a clean analogy. It's just that with only that dumb narration and the following gameplay, there isn't enough information in the trailer to make that obvious. I could be wrong, but I'm anticipating that the world will be a dystopian exaggeration of things many people (including those who actually go on these shootings) find wrong with it, with the principle conflict being what happens when the player thinks "He has a point..." after getting more background on the world. But that's just speculation in the vacuum of more information.
Also, on the topic of the developer controversy.