Bocchi no Ningyohime

Ever feel like your existence does not matter? Ever feel like no one would care if you died? Izumi Hoshi is a pessimistic high schooler ready to kill herself by jumping off a bridge. Turns out that drowning is pretty painful, so she chickens out. Takuto Kurihara saw Izumi jump from the bridge, so he tries to save her. It turns out that Takuto has the personality and skills to bring out Izumi's hidden talent that she never knew she had.

(Source: MangaHelpers)