SPOILERS AHEAD, fair warning....
The most hate I see seems to stem from Natasha referring to herself as a monster because of the way she was turned into an assassin early in life, at some sort of hardcore ballet school. Part of the assassin program was sterilization, and for some reason when the character refers to herself as a monster (meaning fellow monster, including Hulk), they read that as because she was sterilized, and not, you know, because she became an unstoppable killing machine, which is sort of, you know, fucking horrific. They also seem very butthurt that Hulk sort of "saves" Black Widow toward the end of the movie, because that's part of his job. You know, like he saved Iron Man at the end of the first movie, and nobody cared about that. Teammates shouldn't help other teammates, folks!
There might also be some butthurt over Scarlet Witch becoming temporarily grief stricken when her brother gets killed in the heat of battle (I told you there were spoilers, fool!) and turns into a bit of a loose cannon. But they very clearly establish how close these two are (were). I mean, really well establish.
The left wing Tea Party (as Patton Oswalt dubbed them recently) is psychotic.
They misread her as calling herself a monster because she has been sterilised, its not, but even if it was, that would interesting story telling, its not exactly a stretch to say the character is to be further developed.
Taking her out of the last fight just as the action starts is mean if it was going to be the more high profile, almost exclusively male team taking the glory. But then its quickly followed by all the human characters leaving, then onto the super powered characters like captain America. Towards the end of the fight there's only two or three people on it.
The whole sequence was a very deliberate and calculated inversion of what we saw in Man of Steel which was nice in that it was showing they were placing saving human life even above defeating the villain.