i think its a shame that arya is so frequently labeled as "independent" bc it fails to capture the duality in her storyline between dependence and independence. contrary to popular belief arya depends on other people and her arc revolves around that profound need in a violent, desperate, wartorn world where connection is difficult (seemingly impossible at times) to maintain.
in the most basic context arya is a 9 year old child in the beginning of the story. she, obviously, depends on other people. in a sane and safe world she would be cared for by her parents - or at least competent adults. but she is forced onto the streets where she has to fend for herself. she goes hungry and risks assault but she is able to survive. when she gets picked up by yoren she becomes a (temporary) recruit of the night's watch where arya herself recognizes that they provide her with protection, food, and company. this is a similar dynamic to the one we see with her friends later. they provide arya with crucial companionship if nothing else. arya highly values gendry and hot pie. she forces them to escape harrenhal with her - she did not flee alone! and she stays with them despite the fact they slow her down and jeopardize her personal goals.
other people can be liability too. they can make you vulnerable and they can leave you. arya knows how it feels to be left behind. most of her family, to arya's knowledge, have been violently murdered. her allies and friends have left in a variety of ways. arya believes she is the lone wolf - not because she wants to be but because she is desperately alone. we see her try to convince herself that she is independent; that she doesn't need friends and that she must accept a life without a pack. these are the thoughts of a depressed and traumatized young girl trying to cope with abandonment. this is the condition arya is in when she arrives at the house of black and white where she will be required to forfeit her life to the god of death.
on a thematic level arya's very identity has been dependent on her family, her pack. the loss of this chips away at her sense of self until arya doesn't even know who she is without her father and mother and siblings and her wolf. nymeria represents arya's soul in wolf form and she has amassed a gigantic pack that she leads. arya holds them close in her heart:
And dreamed. That was the best part, the dreaming. She dreamed of wolves most every night. A great pack of wolves, with her at the head. She was bigger than any of them, stronger, swifter, faster. She could outrun horses and outfight lions. When she bared her teeth even men would run from her, her belly was never empty long, and her fur kept her warm even when the wind was blowing cold. And her brothers and sisters were with her, many and more of them, fierce and terrible and hers. They would never leave her. (Arya, ASOS)
this is the only comfort for arya in the wake of the red wedding: a pack that will never leave her.
arya is able to think and act independently. she has a will of her own and a strong one at that. but she is a deeply social character who depends on community. this is her most consistent character trait. arya thrives on her interactions with others. she wants a stable community and we see her cling to that whether its as arya of winterfell or cat of the canals.
the framing of arya as this independent entity is doing her character a great disservice in fandom spaces. its one of the main reasons speculation for her endgame is so weak tbh. arya going off on her own to be a lone wolf is completely at odds with her character and the themes of her story. yes, other people can hurt. yes, they can leave you. but that is the price we pay being connected to one another. arya's character explores this theme more deeply than any other character, i'd argue. the pack survives is her mantra and hers alone.
