Fair enough. Maybe she is close to completing her training. The only thing is that the kindly man still wants her to forget Arya Stark. He can still tell she's lying when she answers that she's "no one". My interpretation has always been that she has to completely forget her past self, her list, her sword, everything if she wants to become a Faceless Man. I admit that it could also be interpreted that he simply wants her to control her emotions so well that he can't tell she's still Arya Stark deep down. I.e. to truly be "no one" to everyone else in the world.
Here's the thing - and perhaps this belongs in another thread - I just don't think she's going to complete her training and become an assassin. In fact, you're partially the reason why I don't believe she'll become a Faceless Man. In your
Faceless Men thread you posed a few challenging questions (the ones just after point 3). I believe those questions will be answered. And, of course, I like to keep things simple and look at it from a practical (technical?) standpoint and simply note that the best way to answer these questions would be to be on the inside of their organization. We need a POV for that and we have one and that's Arya. So that's it: I believe her role will be expose that particular mystery. It doesn't sound too important but it's actually grounded in the deepest machinations of the entire world which makes it huge and gives Arya a huge role to play that doesn't necessarily involve murdering a few annoying and relatively insignificant players (relative to, you know, manipulating who sits the Iron Throne as well as who controls everything in the entire world).