Yeah, I definitely agree with the sentiment that she has a personal grudge with Arya, and that a girl who is no one will not carry a grudge.
That's where I think the Waif comes for Arya, they have this big discussion, then Jaqen appears and either kills the Waif, is killed by the Waif (and Arya finds out that that particular person had been Syrio) or Arya ends up killing the Waif.
I am kind of hoping the waif is just another person further along in her training. If they make the Waif somebody we've seen before (either from Arya's past or from another story) I think I'll be upset.
As for the Faceless Men only killing bad people, no. I don't buy that at all. Morality is subjective, first of all. Second of all, I don't understand how a guild of assassins can have a moral code. I understand they had humble beginnings and good intentions of freeing the Valyrian mine slaves, but I am in full belief that if a price is paid to them, they will kill their target.