Arya Stark is one of the most popular characters in A Song of Ice and Fire. She's certainly one of my favorites. Brave, quick-witted, fierce and determined, Arya survives in a world that kills many older and more experienced players using courage, adaptability, intelligence, and, of course, a whole lot of luck.
But she's also, in a way, naive. She's naive about how she can treat Prince Joffrey without receiving severe punishment in return. She's naive about the future she can expect for herself, and naive about the cost of her rebelliousness. Although she rejects every romantic fiction that Sansa adores, Arya loves stories of women warriors, and she invents her own tales of individualism that place her into a similarly perilous position. Readers love her for this naivety, because it pushes against expectations and allows her to treat Joffrey exactly as everyone would like him to be treated. However, escaping the oppressive nature of Westerosi expectations is not as easy as simply deciding not to listen, as the struggles of other "untraditional" women and Arya's own unfolding plot demonstrate. The women of Westeros must either bend to expectations, at least superficially, or find themselves broken.
This post contains spoilers through A Dance with Dragons.
Unlike Sansa, Arya never has any delusions about the nature of Cersei, Joffrey and the other Lannisters in King's Landing. However, when her father is beheaded in front of her and she begins to lose her family members one by one, she is (inevitably) emotionally traumatized by the ordeal. She see torture and pain and death wherever she goes, and she is thrown from identity to identity in order to survive. Sometimes her brutality makes her difficult to like in later books (at least, to me), but it is painfully realistic. She has learnt that human life means very little -- "all men must die" -- and she is willing to sacrifice it whenever necessary. The young girl who was horrified when she stabbed the stable boy is replaced by an agent of death whose ruling principle is, as Syrio says in Game of Thrones, "not today."
The cost of Arya's independence, and of the power to enact revenge, is nothing short of her own identity. Metaphorically, she loses her identity as the idealistic and rebellious girl is overtaken by a need for revenge. In a more literal sense, she skips from name to name, and disguise to disguise, until she joins the Faceless Men and must abandon her roots entirely and become "No One" in order to train as an assassin.
Ironically, the hatred that drove her forwards also helps save her for this complete loss of identity. Arya cannot let go of the need for revenge or the sense of injustice that has settled deep inside her. In a world where individual choice often trumps vows and "honor," where few people are purely wicked or purely good, and where expectation rarely meets reality, Arya cannot achieve her goals by fading away into another destructive kind of subservience. She still feels a connection to Jon Snow, to her once-hated sister in King's Landing, and to the wolf who still prowls in the forests, brutal and wild like her, and this connection keeps a flickering sense of herself alive.
Although they are "as different as the sun and the moon," Sansa and Arya's stories therefore mirror one another. They both struggle out of naivety and struggle to retain their identities. Sansa must pretend to love Joffrey, as she curtsies and smiles and eventually becomes Alayne Stone to survive, and Arya, in taking the opposite path, must also take on identity after fake identity and eventually become entirely nameless in order to stay alive and get revenge. Neither path is better than the other, because they are both terrible options -- and, in the end, neither is really a choice. Sansa does not choose to be sweet and kind and to wish to please those around her, and Arya does not choose to prefer fighting and adventure, yet they both suffer for their actions and personalities. The story of the fake!Arya, combined with Sansa's own experiences in King's Landing, shows that the Stark girls are nothing more than pawns, symbols that can be used and traded by more powerful players, with little concern for who these girls actually are. Yet, more than anything, Arya wants to be an actor. She wants to be active and have an influence on the world. But a young girl cannot be an actor in Westeros, not without great cost, and so Arya finds herself lost in another game, with men who want to turn her into another (more literal) faceless pawn.
If she submits to them, she will lose herself entirely. And without this outward submission, without an acceptance of other's expectations, Westeros leaves little space for her to become anything more.