I have no clue what this story is, all I know is that this is trash but it has an Erotica tag on it and the teacher has a nice body.
Also the MC clearly shows that he has incredible amount of skill and power. So if she truly wanted an out, he's right there and showcased how much of a chad he is in combat. So unless there's something beyond just general blackmail that typically is an unbreakable contract in hentailand. I will just assume this is a hentai that accidentally got marked as a manga.
Then again, it looks like there's something going on. Either some Law of the Jungle thing with master/slave relations based on the summary or if this was a full hentailand story, some national sexual relief law. Probably the former since this seems like it's battle oriented.