If one falls too low, then the suitor gains a "bomb." When the suitor has a bomb, then she'll gossip about the player to the other characters, lowering his relationship with them.
Hatoful Boyfriend is a parody of the dating sim genre.
Popularized by a Let's Play on the website Quarter to Three, Hatoful Boyfriend took the Internet by storm, as shown by a massive amount of fanart and fanblogs on sites such as Tumblr and Pixiv, and helped bring dating sims back into the public consciousness.
The game plays with the expectations of genres: aside from the obvious change in expectations (you date birds), the game is very self-referential and plays with tropes inherent in video games.
Unlike with the Visual Novel genre, Dating Sims place a lot of emphasis on rpg type elements, such as statistics, shown by keeping a girl's affection levels up and boosting up stats (intelligence, strength, etc.) through taking classes or participating in activities.