The author really fucked up when they went with a false rape accusation threat as the set up. If they'd have just used blackmail with a secret or compromising photo then the female main character wouldn't be coming off as a complete psychopath.
The main character's reactions to her and what she's doing are also off. He should absolutely hate her for, not only threatening to ruin his life if he doesn't obey her every command, but also forcing him to do stuff that could ruin him anyway.
This all gets compounded if the development that I think is going to happen happens. That being that she's been intrested in/in love with him ever since seeing him do something "gentlemanly" back in middle school, and this whole situation is just a pretext for her to get closer to him. If that situation does happen then she really is a psychopath.