Not a novel reader, but from what I gathered from the anime and from the manga, Natsukawa is just stupid.
She's inconsiderate of Wataru's feelings, takes him for granted, and when he distances himself from her she doesn't think there's something wrong with HER attitude towards him, she thinks there's something wrong with HIM (hence the scene with him on the school rooftop talking to his sister and Natsukawa butts in belittling him in front of Kaede), and she thinks she needs to correct his behavior instead of looking at herself in the mirror.
She goes from "I was mean to him" to "I won't let you get close to my sister" because Wataru was physically near her and she felt like things had gone back to status quo, where she would say stuff like that and he would just stick to her saying how much worships the very air that she breathes.
So it's not uncharacteristic of her to behave that way, she felt bad because, in a rare moment of introspection she managed to realize she was at fault, but since things seemingly turned back to status quo for a moment, she decided she had no need to change and went back to pushing him away. Then he went away and now she's too stupid to realize why.