Jaqen and Arya have a special bond since the day Arya saved him. She gets invited in to the Faceless Men and receives training. Then she couldn't complete her mission and decides to leave the Faceless Men to go home. When the Waif reports back to Jaqen that Arya has failed, we see that he is disappointed and he only says "Shame, the girl had many gifts". He goes back to his 'work', only to be interrupted by the Waif who wants to go assassinate her, he only gives a nod and adds not to let her suffer. So he wasn't the one to give a hit order on Arya.
In episode 8:
Arya kills the Waif, then goes after Jaqen, she tells him "A girl is Arya Stark of Winterfell and I am going home". To which Jaqen smiles, almost as if that was what he intended when he trained Arya.
Supposing there is a hidden assassin group, I doubt they will recruit someone, train that someone, and would allow that someone to leave when they want to leave with all the investment the group has put into training that someone. Not to mention the secrets that someone would be taking with them. Unless that was their intention in the first place.
Jaqen could easily kill Arya, even if she had a sword pointed at his heart.
Why would he let her go?