(Spoilers Extended) The Waifs Lie, Faceless Men Theories, and something people here seem to frequently not get about the Faceless Men.

So people on this sub seem to completely miss a huge point about the Faceless Men and to examine what that is we will first talk about this scene from Arya's chapter in AFFC:

"Who are you?" She did not expect the waif to answer, but she did. "I was born the only child of an ancient House, my noble father's heir," the waif replied. "My mother died when I was little, I have no memory of her. When I was six my father wed again. His new wife treated me kindly until she gave birth to a daughter of her own. Then it was her wish that I should die, so her own blood might inherit my father's wealth. She should have sought the favor of the Many-Faced God, but she could not bear the sacrifice he would ask of her. Instead, she thought to poison me herself. It left me as you see me now, but I did not die. When the healers in the House of the Red Hands told my father what she had done, he came here and made sacrifice, offering up all his wealth and me. Him of Many Faces heard his prayer. I was brought to the temple to serve, and my father's wife received the gift." Arya considered her warily. "Is that true?" "There is truth in it." "And lies as well?" "There is an untruth, and an exaggeration." She had been watching the waif's face the whole time she told her story, but the other girl had shown her no signs. "The Many-Faced God took two-thirds of your father's wealth, not all." "Just so. That was my exaggeration."

Arya correctly guesses the exaggeration but not the lie. So what is the "untruth" that she tells in this story? The lie is that she claims she "did not die" because the person she is speaking about is not herself but rather this is the story of the person whose face she is wearing. And this brings us to the point people keep missing about the faceless men: they are no one. To be a faceless man is to give up all sense of identity and it's very likely that no faceless man ever wears his real face or assumes their "real" personality. They are "faceless". The untruth in this story is that the girl did die (eventually at least) and her face is being worn by the faceless man talking to Arya.

Where people keep getting this wrong is when we talk about the faceless men as if they are individuals with distinct personalities, when they are not. So let's see an example of this by examining the refutation of one of the more popular faceless men theories:

Jaqen = Syrio. SO upfront I will say I don't necessarily believe this theory, i'm just going to use it as an example of how people misunderstand faceless men. So this theory states that Syrio and Jaqen are the same person because as soon a Arya loses one mentor teaching her to be a little badass (Syrio) she quickly meets another one (Jaqen). A common criticism of this theory is that if Jaqen is Syrio then why did Jaqen spend time masquerading as the First Sword of Bravos. Well that is kind of missing the point - If Syrio was Jaqen (or any faceless man) then there was no Syrio, he is just a face and personality being worn by a faceless man - maybe there was a man called Syrio and maybe was the first Sword of Bravos but that could have been 100 years ago or never at all - he is just a disguise. Another problem people bring up is why Jaqen would allow himself to be captured just to get near Arya - this is because Jaqen isn't a real person either just another personality being worn by a faceless man. Maybe that face belonged to actual criminal named Jaqen who a faceless man just traded places with, or again maybe he is a total invention, but either way it doesn't matter because Jaqen isn't Jaqen he is no one.

But more importantly this applies to all faceless men - every name and personality we associate with a faceless man (Jaqen, the Waif, the kindly-man, the Alchemist) is not who they are because they are no one what we see is almost certainly not their real face or personality or name.

Look at they are trying to do to Arya in her training - they are essentially trying to kill her personality, all semblance of Arya Stark, and make her "no one" they want her to shed everything and where other names, other personalities, other faces. That is what it means to be a faceless man, and it is right there in the name - they are faceless men - those without an identity to call their own.