The whole thing lies in the fact that they are not blood related: Masato's father married Miyuki's mother, and when her mother died she went to live with him overseas. The story starts when Miyuki comes back to live with Masato.
He's not sure if she knows they are not blood related, so he behaves as if they were: she has no other relatives and he doesn't want to hurt her by making her realize she has no "real" family in the case she didn't know.
On a side note, Miyuki is the name of Masato's girlfriend too
And yeah, the late 20s teacher and mature policeman with the "loli" complex are quite funny