Arya never hates Sansa or any other traditionally feminine woman for being able to sing, dance, sew, and mind their courtesies. She hates herself for not being able to do those things. She thinks her family would love her more, or that Catelyn would have been more willing to ransom her, if she was more feminine and could do those things.
On the other hand, you have Sansa who wishes that Arya was a bastard and that she could have another - more feminine - sister.
Why couldn't Arya be sweet and delicate and kind, like Princess Marcella? She would have liked a sister like that.
Sansa could never understand how two sisters, born only two years apart, could be so different. It would have been easier if Arya had been a bastard, like their half brother Jon. She even looked like Jon, with the long face and brown hair of the Starks, and nothing of their Lady mother in her face or her coloring. And Jon's mother had been common, or so people whispered. Once, when she was littler, Sansa had even asked Mother if perhaps there hadn't been some mistake. Perhaps the grumkins had stolen her real sister.
- Sansa I, AGoT
Sansa is ashamed of Arya for being a tomboy instead of being more feminine.
They don't know me, Arya realized. They don't even know I'm a girl. Small wonder; she was barefoot and dirty, her hair tangled from the long run through the castle, clad in a jerkin ripped by cat claws and brown rough-spun pants hacked off above her scabby knees. You don't wear skirts and silks when you're catching cats. Quickly she lowered her head and dropped to one knee. Maybe they wouldn't recognize her. If they did, she would never hear the end of it. Septa Mordane would be mortified, and Sansa would never speak to her again from the shame.
- Arya III, AGoT
Sansa attacks Arya for not being good at something traditionally feminine.
Sansa threw her head back in disdain. "You?" You couldn't sew a dress fit to clean the pigsties."
- Sansa III, AGoT
Sansa thinks that Arya was unsatisfactory as a sister because she wasn't feminine.
Sister. Sansa had once dreamt of having a sister like Margaery; beautiful and gentle, with all the world's graces at her command. Arya had been entirely unsatisfactory as sisters went.
- Sansa II, ASoS
Now where does Sansa get her sexism from? Catelyn (and Septa Mordane).
Arya wonders if her family would even want to ransom her because she's not traditionally feminine.
"What if my brother doesn't want to ransom me?"
"Why would you think that?" asked Lord Beric.
"Well," Arya said, "my hair's messy and my nails are dirty and my feet are all hard." Robb wouldn't care about that, probably, but her mother would. Lady Catelyn always wanted her to be like Sansa, to sing and dance and sew and mind her courtesies.
- Arya VII, ASoS
Catelyn telling Arya she could be pretty...if only she were more feminine.
Her mother used to say she could be pretty if she would just wash and brush her hair and take more care with her dress, the way her sister did. To her sister and sister's friends and all the rest, she had just been Arya Horseface.
- The Blind Girl, ADwD
