I love that what ultimately led to Littlefinger’s downfall is the fact that he didn’t know Arya.
This is a man who has built his life and his entire plan around manipulating the Stark/Tully women. He has always believed that he knows them well enough to predict every move they will make and use them accordingly.
But he never bothered to pay attention to Arya because she didn’t remind him of Cat. His own creepy obsession with Cat blinded him to Arya’s personality, motivations, and talents. She didn’t appeal to him. She was more Ned than Cat, and he already beat Ned, so what threat could Arya be?
I don’t believe that Sansa and Arya were on the same page this whole season. There was real tension and anger between them, and I think that when Arya walked into that hall, she didn’t know for sure what Sansa was going to do.
But Sansa knows Arya. And Littlefinger’s failure was that he thought he did too.
Arya would never want to be Lady of Winterfell. Sansa knows this. She has always known this, because despite the lying, despite the faces, she knows her sister at her core. Littlefinger implying that Arya would want to rule the North was the final push Sansa needed to know she was ready to outplay him.