This is discussed in the after-episode conversation with the writers. They are showing that Arya and Nymeria (like most of the Starks and their Direwolves) share personality traits.
They reference back when Arya is talking with her dad about being a "exemplary woman" and she says "That's not me". When she meets Nymeria again, she realizes that, as much as Arya has made a new place for herself, so to has Nymeria. She is no longer Arya's pet. She is her own wolf and has found her own life. This is why Arya says "That's not you" - she realizes that her connection with Nymeria is gone and she needs to move on.
It's discussed in The Independent here. Not sure if the video is generally available outside of HBO.
During a post-episode discussion, showrunners David Benioff and D.B. Weiss explained how the phrase was a callback to season one. One early episode sees Ned Stark tell his daughter that she will one day be a lady and get married, to which she replies: “No. That’s not me.”
Benioff describes how Arya wants Nymeria “to come back home with her and be her loyal companion again. But Nymeria’s found her own life.”
The video is here: