While we’re examining the role both Stark sisters play in relationship to patriarchal values, as an attempt to better understand their relationship to each other, the story as a whole, and to themselves, I’d like to see us remember that Sansa is also a child. Yes, she is older. Yes, she is better at playing the role demanded of her. But just as Arya is intimidated by Sansa being better at feminine things, Sansa is intimidated by Arya being loved and valued despite not committing to those things. Internalized misogyny and policing the patriarchal values she is taught are a part of it, but just as Arya is hurt by her mother potentially thinking she’s dirty and unsalvageable, Sansa is hurt by a muddied Arya, carrying weeds, being hugged, loved, and cherished, while she, the eldest daughter who finds herself betrothed to a prince in the beginning of our story, cannot risk appearing so human.
The girls have memories of gorging themselves on cakes, snowball fights, being scared and scaring each other, so their home life was very typical to any sibling relationship or family relationship. I think the crux of it is the fear of falling out of familial roles and familial expectations, ultimately. So I think it’s shortsighted to not mention how their perception of what Catelyn and Eddard expect of them is a heavy part of it and pretty baseless to call either of them a bully.
And on the whole I don’t believe in a narrative that has to say, “yes, they made mistakes” or “yes, X was mean to their sister/brother Y” in order to defend a child or a social narrative in a fantasy novel. Sansa laughs when her friends call Arya Horseface. Arya hurls entire fruits at Sansa. They aren’t bullies, they’re children, under an immense amount of pressure as part of a noble family.