Speaking about the Faceless Men, they're hypocrites. Fullstop.
Their whole thing is becoming No One, people who don't actually have identities and only serve on purpose: to become whoever is required to kill their target.
This is almost instantly shown to be bullshit from the very first scene that we find out the Faceless Men are even a thing when we see that Jaqen H'ghar not only has a soft spot for Arya but is then disappointed when she turns him down to go off to Braavos with him. This soft spot is carried over when she finally does go to Braavos to train with them when she's given multiple chances and it's clear to him and the Waif that she's still Arya and not No One. Anyone else would've either been kicked out or killed but he keeps giving her chances because she likes her, again, going against the whole concept of being No One.
The Waif, too, is shown to be a hypocrite. From day one she hates Arya because she feels she's not committed to becoming No One but would No One who is No One hold that much ill will togethers another person? Holding such emotions is what the Waif feels, as an individual, again, she's a hypocrite.
Even after everything is said and done Jaqen STILL gives her another chance after she kills the Waif and would even allow her to stay with the Faceless Men. When Arya refuses and leaves, at this point another Faceless Men would probably kill her, but Jaqen proudly smiles at her and nods at her, letting her know he was allowing her to leave. He does this all because Jaqen has taken a liking to Arya.
The Faceless Men are like a company that seems to have their shit together, you join, and realize there's a ton of office politics and no one knows what the fuck they're going.