My head cannon says this behavior is approximated by step-parents being shitty to their step kids so that their own kids get preferential treatment. But I have no proof, just life experiences.

Oh boy do I have bad news for you:

Filicide overwhelmingly linked to male perpetrators who ‘deeply believe their actions are justified’, experts say

Filicide

It is not exactly the situation you mentioned, but I think it is at least highly related?