I think the whole "That's not you" was Arya acknowledging that Nymeria was a wild wolf and she was not going to be Arya's pet.Wizard said:
Is it possible that Nymeria didn't recognize Arya?
A lot of time has passed and although Arya is Arya again she spent so much time training to be "no one".
At the same time, I wonder if the dual meaning is Arya realizing that she is not a "wild" wolf and she is going to return home to her family. I think Arya's arc is going from this willful child who wanted nothing more than to be done with her family and Winterfell, to somebody who now respects and appreciates the bonds of family and a place you can call home. That is not to say I think Arya will put on a dress and be all prim and proper, but I do think she is going to go and help Sansa and Jon as much as she can, in her own unique way.
So, the "that's not you" was acknowledging that Winterfell and being her pet were not Nymeria's place in the world, but also acknowledging that going it her own way and checking off her list and ignoring her family is not Arya's place in the world, either. (or I guess it could be the opposite, as somebody else said, and Arya is going to start heading south again. I can see that reading on it, as well).