Monika is the most tragic of all the characters. She is put into an impossible situation where she has to do unspeakable things. She has become completely self-aware (something about being president of the club) and she does not experience time the way we do. Also, based on her poems, when the game is off, she is bombarded and overwhelmed with information. This flood of information is torture, and as we don't know how she experiences time, this torture could have felt like an eternity. She is forced to do the horrible things to her friends, or return to the torture. She is much closer as a partner because she “is real” and knows you are too. Her desperation is the most real. It's crushing. She really can't even marter herself in this situation. It's the reason I agonized over deleting her. And then, she allows you to delete her and gives you back the other Doki's. She didn't have to, but she did, for you.
I wept for Sayori.
I wept for Yuri.
I cried for Monika.
People who don't like her (IMHO) either can't get past the pain they feel for their favorite Doki that isn't Monika, or don't fully grasp what she goes through, and the pain/desperation that she feels / forced to endure.
As well, she is new to sentience, and like learning to ride a bike, she falls sometimes.