Ore no Imouto ga Konna ni Kawaii Wake ga Nai

Kyosuke Kosaka, a normal 17-year-old high school student living in Chiba, has not gotten along with his younger sister Kirino in years. For longer than he can remember, Kirino has ignored his comings and goings and looked at him with spurning eyes. It seemed as if the relationship between Kyōsuke and his sister, now fourteen, would continue this way forever. One day however, Kyosuke finds a DVD case of a magical girl anime which had fallen in his house's entrance way.

(Source: Crunchyroll)