So when Age of Ultron came out, there was the whole thing about Bruce and Natasha being a couple, or more specifically, the idea that Natasha felt they were both monsters, and that she was a monster because the Red Room had made her incapable of having children. I doubt Whedon specifically meant a woman is a monster if she cannot conceive, but that's how it came off, and this was understandably not received well by some people. And it's such a dumb way of going about it. Especially because there was a so much better way to make that comparison already waiting.
In the first Avengers movie, they establish this idea the Hulk is sort of a survival mechanism for Banner. Stark raises the point that the amount of radiation banner was hit with should have killed him, but instead he became the Hulk. Banner asks if Stark is suggesting the "other guy" saved him, and seems both skeptical and scornful (mostly of the idea he should be grateful). Later Banner admits he tried killing himself, and the "other guy" spit the bullet back out. Some part of Banner wants to live, and finds expression in this monster.
Now you've got Natasha. We know, again from the first Avengers movie, she feels there are things she's done she has to atone for, or at least balance some scales (the whole "red in her ledger" bit). We know from The Winter Soldier that she had hoped, even though she was doing the same sorts of things she used to, that doing them for SHIELD meant she was doing something better, and she was distressed to see that it really wasn't working out that way. You could even interpret her willingly releasing all those SHIELD files, including the ones about her and her activities, as part of her trying to deal with her past.
Then, in Age of Ultron, we get a glimpse of her training in the Red Room. Of her being caught in that headlock and not being able to get loose, tapping out, and being reproached by her teacher. And yet, she became the best student the Red Room ever produced, right? At some point, Natasha decided that to survive, she'd do what was necessary to that end. It could be argued they had successfully indoctrinated her to the idea she was simply an unimportant tool of theirs, but I still think on some level she would have to want to survive to not merely pass, but become as great as she is. Once she was out on missions, that continued. She had to do awful things to complete her missions, but she has to complete them to survive.
Which leaves her with the realization of all that she did, she feels guilt over, because she also wanted to survive. Whether it's her being too rough on herself or not, her perception would be that, like Banner, her survival instinct took the form of a monster. They've both tried to turn that to something good, while fearing that it's never going to be enough.