This article contains spoilers through to the end of Mockingjay
Katniss is the protagonist of a powerhouse dystopian/action/war series that just broke records at the box office (something that conventional Hollywood wisdom would tell you should be impossible), and yet she's one of the most unlikeable female protagonists I've ever seen. And, weirdly, her unlikeableness is one of the most likeable things about her.
Because, in the end, Katniss commits the cardinal sin for a female character: she isn't very nice.
Katniss cares about herself and a select group of people (Prim, Gale, later Peeta and Rue), and although she is horrified by the deaths or suffering of others, she knows where her own priorities are. She is entirely unforgiving of others. She's incredibly judgemental. Perhaps worst of all, she's confused about her feelings for Peeta (the boy the Capitol seems to have forced on her) and Gale (the rebellious friend she feels she should like), and she's not afraid to take her time exploring and figuring out her feelings -- or even ignoring them entirely, when more important things are at stake. After Peeta has been tortured and hijacked by Snow, she treats him sharply and goes out of her way to hurt him, almost in revenge for him unwittingly hurting her. She's willing to ask Haymitch to die so that Peeta can live. She's not as harsh and closed off as characters like Johanna, but they have a lot in common. She doesn't want friends or allies. She simply wants to survive, and to bring the most important people with her.
She's also brave and defiant and caring in her own way, and she always does what she believes to be right, but these traits are not wrapped up in a generosity of spirit or a softening niceness. As the books say, good people do not survive the Hunger Games, except perhaps Peeta. She won't join the Careers and hunt the other Tributes down in a pack, but she will kill them when she has to, and one in a horrible, Tracker Jacker-filled way. She's deeply flawed and full of anger, and those are traits that a female protagonist is never supposed to have.
And despite her best intentions, Katniss is not in control. She's not the bold, brave leader driving the rebellion. She's a pawn, fighting the control of others -- first of the Capitol, then of the rebels and District 13. In many ways, she's not the hero. She's rarely kept informed, and she often completely misinterprets the actions and intentions of those around her.
Katniss is also driven almost entirely by impulse. She volunteers to protect her sister without any forethought. She gets Haymitch's attention by losing her temper and stabbing the table with a knife. She kills Rue's killer in rage and grief, she attacks Haymitch when she finds out Peeta was captured, and she shoots President Coin when she remembers Snow's words. She's not much good at thinking ahead or viewing things objectively, and when asked to give speeches or generally perform in any way other than through impulsive emotion, she fails miserably.
And, perhaps most surprisingly of all, Katniss is allowed to be damaged. She is emotionally scarred by what she has gone through. By the second book, she is having flashbacks to the arena, is plagued by nightmares, and is willing to take whatever comfort Peeta offers without worrying about what it means to him. By the third book, she is losing her mind entirely. From a narrative perspective, this causes lots of problems, as Katniss is knocked out, confused or locked away for many of Mockingjay's important moments. But from a character perspective, it's fascinating. Katniss has been responsible for so much, without ever asking for that responsibility. She's asked to be a figurehead, but any real control is wrested from her. She loses most of the few people she cares for, and kills many people herself. And far from shouldering the pain or being quiet and delicate in her grief, she goes insane. She screams and fights. She turns catatonic. She tries to starve herself to death. She uses alcohol and morphling to numb the pain. In the end, her experiences are too much for her.
All together, Katniss is a female protagonist who is selfish, vindictive, reluctant, furious, impulsive, and even cruel. She is, ultimately, a realistic portrayal of a starving, oppressed girl who barely survives a horrific war in which she's made to play a huge role and over which she has very little control. And so, despite her good qualities, despite her sense of justice and the kindness she can show, she is miles away from what is normally considered acceptable for a female character.
Yet she's the star of one of the biggest book series and film series of all time. Figure that one out.