Arya does not kill Jaqen. In fact, Jaqen becomes a significant mentor figure for Arya and plays a crucial role in shaping her journey and skills.
After saving Jaqen and his fellow criminals from a burning wagon, Jaqen offers Arya three deaths as a token of gratitude. Arya initially uses these offerings to eliminate three people on her list of people she wants dead. However, it is important to note that she does not directly kill Jaqen himself.
Jaqen is a member of the Faceless Men, a secretive and highly skilled group of assassins who worship the Many-Faced God. Intrigued by Arya’s potential and her desire for revenge, Jaqen invites her to join their ranks in Braavos. Arya accepts his invitation and travels with him to the House of Black and White, the headquarters of the Faceless Men.
Under Jaqen’s guidance, Arya begins her training in the ways of the Faceless Men. She learns to adopt different identities and faces, to become a skilled assassin capable of killing without leaving a trace. Jaqen teaches her various techniques, including the art of deception, poisons, and the ability to strip away her own identity.
Throughout their time together, Jaqen challenges Arya’s beliefs and tests her resolve. He pushes her to let go of her personal vendettas and embrace the notion of being “no one,” a faceless servant of the Many-Faced God. This training transforms Arya and helps her evolve into a more formidable and complex character.
While Arya’s journey with Jaqen is filled with personal growth and valuable lessons, their paths eventually diverge. Arya’s strong sense of self and her refusal to completely let go of her own identity clash with the Faceless Men’s teachings. As a result, Arya decides to leave the House of Black and White and continue her own journey as an individual.
Although Arya doesn’t kill Jaqen, their relationship is crucial to her development as a skilled assassin. Jaqen’s teachings and influence shape Arya’s abilities and mindset, setting her on a path that ultimately leads her to become a force to be reckoned with in the Game of Thrones universe.