me @ this question:

largely because you pulled something random from the books and something random from the show and then called her ~insanely problematic~. pick one battlefield: the books or the show. i’ll not address the show because the show is bullshit and i’m amazed you haven’t realized that yet.
To answer your general question: why do people like Arya? Well, she’s compassionate, she loves people for who they are, she stands up for those weaker than her, she’s resilient, she’s intelligent, she’s emotional, she cares, she’s willful, she’s brave (so, so brave), and is stronger than anyone gives her credit for. I could go on and on and go into the details, but you’re clearly not interested in that. But I do want to address one thing…
In the books she prioritised killing a perfect stranger over tywin.
Who was that perfect stranger? Oh yes, he was Weese, who physically abused Arya during her time at Harrenhal, hitting her over nothing, and a man who she described as being “nearly as scary as Gregor Clegane” and who she lived in fear of. A perfect stranger? No. She knew who he was. She knew he was beating her and her friends. So she had him killed.
Alright, what about before Weese? We’d be talking about Chiswyck, a man who tortured smallfolk and bragged about gangraping a thirteen year old in front of her father and killing her brother. Who, while bragging, laughed about it and made jokes about it. Did Arya know him very well at all? No. But Arya saw a chance to make this disgusting man pay, to prevent it happening to other girls, and she took that chance. It’s not always about cutting off the head of the snake. Sometimes attacking the body is just as necessary.
In any case, Arya regretted her decision to have Weese and Chiswyck killed very soon after she whispered his name to Jaqen:
A shiver crept up Arya’s spine as she watched them pass under the great iron portcullis of Harrenhal. Suddenly she knew that she had made a terrible mistake. I’m so stupid, she thought. Weese did not matter, no more than Chiswyck had. These were the men who mattered, the ones she ought to have killed. Last night she could have whispered any of them dead, if only she hadn’t been so mad at Weese for hitting her and lying about the capon.
Lord Tywin, why didn’t I say Lord Tywin? Perhaps it was not too late to change her mind. Weese was not killed yet. If she could find Jaqen, tell him…
But emotion is what drives Arya. She is willful, she gets angry quickly, and she acts fast. That sometimes works in her favor, and sometimes saves her. But Arya saw these smaller villains, experienced their abuse firsthand, learned of their other abuses, and made the quick decision to see them killed. Sure, she could have had Tywin killed then and there, but wasn’t his fate. But I wouldn’t say that Weese and Chiswyck didn’t deserve what they got, I recognize that Tywin’s story would never have ended so early, and I’m glad for Arya’s anger and compassion. Those are two of the many characteristics that make her so likeable.