Beyond The Boundary (Kyoukai No Kanata)

This story is not mine. I just made the translation. So no hate.
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One day, high school student Akihito Kanbara instinctively goes to save his fellow schoolmate, Mirai Kuriyama, from committing suicide. Following his pleas, Mirai suddenly stabs Akihito with a sword formed out of her own blood and is shocked to discover that Akihito is an immortal "half-youmu"-the offspring of a supernatural creature, called a youmu, and a human. After learning that Mirai is a Spirit World Warrior (異界士 Ikaishi?)-specialists who protect humans from being affected by youmu-and the last surviving member of her spirit hunting clan, their lives become intertwined as Akihito seeks to help Mirai gain the confidence to kill youmu so that she may stop attempting to kill him as practice.

In Beyond the Boundary, youmu (妖夢 yōmu?, alt. Dreamshade) are supernatural creatures that appear throughout the series and can only be seen by those with a supernatural affinity. They are said to be the physical materialization of human animosity such as negative emotions including hatred, jealousy and malice and therefore as long as humans exist, youmu will continue to exist. They can exist in many types of shapes and forms with some even having a human appearance. There are also rare cases when a youmu and a human mate and produce offspring called Half-Youmu (半妖 Han-Yō?, "Half-Shade"). Most youmu are relatively docile and coexist with humans without them even aware of their presence. However, there are times when a youmu's behavior upsets the balance, so the Spirit World Warriors are sent in to kill them. Upon death, a youmu produces a Youmu Stone (妖夢石 Yōmu Ishi?, alt. Dreamshade Stone) which can be appraised and traded, hence providing a source of income for a Spirit World Warrior.