My thoughts on Katherine Shalazar as a character.
Okay, I feel like out of all the guardians, Katherine would be the only one not to hold a grudge against Pitch. What I mean is that Jack isn't the only one who has an interesting relationship with Pitch. If not more than Katherine, because they've known each other longer, there is a definite history between them.
In the books, Katherine always had a special interest in Pitch because of the valiant person he was before back in the golden age and the person who is now suffering under the title "king of nightmares."
Yes, Pitch kidnapped her in books 2, 3, and 4. But she would always genuinely empathize with him. Feeling like an outcast herself, she associated her loneliness with his. I feel like, because she knows what kind of man and father he was back in the golden age, she would fantasize about that personification of him to fill the void that Ombric could not.
She also told everyone in Book 3 not to kill him, not because it would make us no better than he is, but because she literally didn't want him to die. To her, he was still a person who mattered despite his actions.
It was like that scene from Pocahontas where she laid her head on John Smith's head, asking her father and her people to spare him.
I feel like Pitch and Katherine could sense a genuine interest in one another. Pitch has no problem hurting anyone in the book series, especially children, but I know at first, he was planning to gaslight and use Katherine's insecurities against her. But somewhere down the line, he let something inside himself throw a monkey wrench in his own plan and allowed himself to feel somewhat delighted to have her as his own daughter. Feeling her sense of loneliness and filling the void he thought he had long forgotten or snuffed out.
Whether she'd like to admit it to herself or not, Katherine was somewhat interested in the small notion of being his daughter, and maybe it comforted her in a way, sparking her interest in him.
They both lost families—one who sorrowfully tries to forget and one who painfully tries to remember. They bring that out in each other.
I mean, Emily Jane would not have felt as threatened by Katherine being his daughter if she didn't feel Pitch was somewhat attached to Katherine.
Welp, that's my hot take~