05-09-2016, 05:28 AM
It's both. On the one hand, they're looking for people who are willing and able to kill - and being able to attack and defend while blinded can be very useful in that regard. So that part of it is "initiation" or training. But on the other hand, they aren't interested in those who have personal or emotional motivations for killing - and since Arya stole the face in order to kill Meryn Trant for the sake of revenge (rather than as an act of devotion to the Faceless God), this was a serious breach. So that part of it is "punishment."
I'm curious as to whether they'll ever really make Arya "forget" herself (and thus become truly "faceless"). We're at the point now where the show has caught up with the books, so I don't have any "inside knowledge" about Arya's future. I don't recall how much the show has gone into the origin and history of the religion of the Faceless One (or even if it's gone into it at all), but there's a bit about it in the books (it started as a mercy cult in the slave mines of ancient Valyria).