Manga by author Kusunoki Kei

Popular high school student Suwa Daisuke has no interest in dating newcomer Aikawa Hinako, a quiet loner. That's because she recoiled from his flirtatious touch, and he took it as a personal affront. Daisuke informs one of his buddies that he wouldn't date her, not knowing Hinako was listening. Daisuke's attitude changes after he accidentally hears her confession in an abandoned church; she's been sexually abused by her stepfather and has given up a child for adoption. His former annoyance turns to compassion and concern. Hinako is unaware that he knows her terrible secret. Believing him to have no romantic interest, she becomes more relaxed and comfortable in his company. Their relationship faces a lot of obstacles, including jealous classmates.

Shingo Chiryuu isn't much different than any other guy except for one thing... He's afraid of girls. Now he finds himself surrounded by girls, including the one whose attack originally instilled the fear in him, as he attempts to cure himself of his gynophobia.

A demon boy who lacks horns on his head wields the cursed blade "Onikirimaru", the one weapon that can slay a demon, in a never-ending battle with the demons that haunt Japan during the age of the samurai.Behind the stories of Oda Nobunaga, Toyotomi Hidetsugu, Ishida Mitsunari, and the other famous generals of the Japanese civil wars lurk secrets and demons...An astonishingly deep story about these demons and the sword Onikirimaru!And this also includes the secrets of Onikirimaru's birth, which readers have always wanted to know.The legend of Onikirimaru explains clearly how Onikiri was born, and the hidden secrets of his past.Behold the battle between the darkness of the age of the samurai and Onikirimaru, as drawn by popular woman's author Kei Kusunoki!

From ANN:There was once an ogre (oni) mother who gave birth to a human-looking child. Instead of an ogre's horn, this child was born with a sword in hand called the "Onigirimaru" or Ogre Slayer. He has no name and is only refered to by the name of his sword. Though he appears human, he is pure ogre.Believing that he will become human once all of his kind vanished from the world of humans, he sets out on his destiny to slay all of his kind. Even now, in the mother world of Japan, he is still out there slaying ogres.