There's no getting around it: Cersei Lannister is a horrible person. Although, thanks to the extreme cruelty of some of the series' villains, she isn't the worst character in A Song of Ice and Fire, she is ruthless and petty and cruel, and she appears willing to sacrifice anything (except her children) to bolster her own power.
Cersei is also the only "villain" character in A Song of Ice and Fire who gets chapters from her point of view but isn't redeemed or made likeable in any way. Although readers may have different reactions to Jaime in A Storm of Swords and Theon in A Dance with Dragons, the books certainly attempt to make them into compelling, sympathetic characters, but Cersei's chapters in A Feast for Crows only confirm the idea that she is an unhinged, vindictive, selfish, and spiteful woman.
Yet Cersei is also one of the most intricate and interesting (if also detestable) characters in the series. We just have to dig deeper into her motivations to find the compelling details underneath.
Cersei is far from a feminist character. However, she is a fascinating character to examine from a feminist perspective, because her entire life (and much of her personality) is a reflection of the misogynistic nature of Westerosi society. She's an ambitious woman who has had to fight against limitations her whole life, and who has been made hard, cruel and bitter as a result.
Even as a child, Cersei is portrayed as bold and haughty, bordering on cruel. She tormented Tyrion, fearlessly put her hand into a lion's cage, and challenged a witch to tell her future despite how terrifying she seemed. Young Cersei seems rather magnificent -- fearless and defiant, destined for greatness -- but hampered, of course, by the fact that she's a girl. She is the only Lannister child with ambition -- Tyrion has the smart, Jaime has the arrogance, but she is the only one who wants power and success -- and she is the one that the world is least likely to take seriously. While Jaime rakes in the glory (and later, the disdain) and Tyrion is left to his own intellectual devices, Cersei is used as a political pawn by her father, with no choice in her life. Despite considering herself to be almost the same entity as her twin brother, she is treated differently -- as lesser -- since birth.
Although the young Cersei seemed to have the scrappiness and rebelliousness of Arya Stark, she also, like Sansa, had dreams of romance. She dreamt of marrying Rhaegar, of being queen and mother to princes, of being powerful and beloved. But, like Sansa, her dreams are destroyed by the harsh reality of life for women. Although she does eventually obtain her dreams of queenship and something resembling power, her marriage to Robert is a debasement. She is sold off to a man who does not want her, who hits her, who hates her, all for her father's political gain. And although she is determined to make the best of the situation, to stay close to Jaime and play her way to the top, she is deeply bitter and full of wounded pride, and this feeds into every aspect of her character.
She does, however, love her children, and will be fiercely protective of them. Apart from Jaime (who, she believes, is actually an extension of herself), they are the only things that she cares for.
One of her most interesting relationships is her cruel kind of mentorship to Sansa Stark. She does not feel sympathy for Sansa for being in a similar (if not worse) situation to what she herself lived through, but she does occasionally feel inspired to pass along twisted motherly advice to encourage Sansa to be tough and heartless enough to survive. Yet her experiences do not make her sympathetic to women in general. If Cersei survived and manipulated and came out on top, then other women must as well, and if they cannot -- if they appear weak, like Sansa does in her eyes -- then they are worthy of all the disdain that the world piles on them.
But Cersei's greatest flaw, and the cause of her downfall, is that she has spent her whole life fighting for every little scrap of power and respect, and she does not know when to stop. She trusts no one. She clings to her power. She is spiteful and vindictive to ensure that no one challenges her, even on petty matters like the death of a direwolf who did nothing wrong. And thanks to the prophecy, and the shock death of Joffrey, she is incredibly paranoid. The more power she gains, the more vulnerable she feels, and she sees enemies in every shadow. She is unable to stop fighting and accept that she has won -- that her son is on the throne, that she is Queen Regent, that others are trying to help her -- because she has been playing the game of manipulation and sabotage her entire life, and she expects that everyone is waiting for the chance to tear her down.
And she has been playing that game, and become so paranoid, because she is a woman. Not because women are naturally more inclined towards manipulation and other sneaky means, or any such nonsense like that, but because these are the only paths to power that are available to her. She must use her intelligence, and her smiles, and her subtle schemes and string-pulling to fulfil her ambition, because if she pursues any direct course, she will be shoved aside. When people discover these manipulations, they disdain her for it. They despise her for seducing potential allies, or for controlling people with smiles and subtle threats, for playing the sweet queen and being a viper underneath, because these traits are both "feminine" and "un-feminine" -- they are the way a woman plays the game, yet they are not considered proper behaviour for a good kind of woman. No good path is available to her, so she makes the best of what she has, dwelling on her pride and vindictiveness to survive.
And then, at the end of A Dance with Dragons, she is punished for her crimes. Punishment by humiliation, stripped naked and made to walk through the streets to show her weakness. It is a very gendered punishment, designed to punish her both for and through the fact that she is a woman. The scene is less about enacting a fair punishment and more about putting her in her place and making her see that she has no power compared to these other, male forces. Despite her struggles and her ambition, she is always a woman first, and that is always something people will disdain. But any attempt to "put Cersei in her place" is, by its very nature, misguided. Cersei will not bow to anyone. After her punishment, after pretending to be meek and accepting of their dismissal, she will be more than happy to build on her bitterness and enact revenge.