Hey, guess what, that "Now a girl is no one" line and the look Jaqen gave was also shitty writing. S6 is when the shitty writing exploded onto the scene.
Keep in mind, prior to that:
1) Jaqen said, "A girl can be no one, if she so desires." And then gave her a mission to poison an actress (again, without a face, without stealth).
2) Then he said "A girl is given a second chance, she will not be given a third."
3) Then Arya fails to kill the actress - in fact, she outright prevents it.
4) Jaqen gives the waif permission to kill Arya, expressing regret because she had skills.
5) The waif gets the complete drop on her, not by stealth, but by being an old woman, and stabs her repeatedly in the gut (which she shouldn't have survived, but the plot armor was thick around Arya even then).
6) The actress is killed anyways, slowly and painfully, because of Arya's trangression. As the waif said, "The Faceless God is owed a name."
7) Then the waif says, "Now he is owed another name." As an audience, we're supposed to think now that the waif's death paid that debt? The waif made no transgression.
8) Then Arya manages to kill her in the dark with a sword she was told to throw away.
9) Then Jaqen acknowledges the utter emptiness in her by declaring her "no one" (which was shitty writing, to suddenly suggest he was okay with Arya's actions).
10) Then that dumbass smirk when she responds "No, I'm Arya Stark, and I'm going home," even though that runs counter to everything the Faceless Men stand for.
See, those last two points are fan service. The audience wants her to be Arya Stark, not "no one." So the shitty writing allowed her to be Arya Stark with some training, and be a badass, without being a soulless murderer (even though that's what she is supposed to be now).
If you dig deep back enough in this thread, you'll find me bitching about that shitty writing even then. Oh wait, I found it for you:
https://www.mmo-champion.com/threads...4#post40869354