I find your last sentence extremely reductive. It's not about whether Min-Ji is a "good" or "bad" character. She's a sociopath willing to do whatever it takes to achieve her goals. She protects Nick primarily to ensure his success as an idol and to give his group the best possible start. But more importantly, Min-Ji "killed" Nick and destroyed his life in order to shape it into what she wanted. So from her perspective, it's logical that "Kim Minah" is her creation and that his life belongs to her. Therefore, if Min-Ji defends Nick, it's not for his sake directly, it's because "Kim Minah" is Min-Ji's property. Attacking Nick is, by extension, an attack on herself. Almost like a yandere, but without the love ...