It's the exact same reasoning that underpins all the men who treat their wives like fuckable housekeepers and whose wives get told LTB on the Relationships board, namely that women aren't people with autonomy and their own dignity and rights, but are subordinate support appliances ("bangmaid" for short, a maid that he gets to shag) who exist to service men and that men are entitled to have such a female support appliance.
This reasoning underpins a whole range of behaviours, from DV, rape, and murder to almost invisible things like women getting out of men's way when walling towards each other and women washing male colleagues' cups at work because the men silently leave the dirty cups next to the sink and the women silently do the dishes because we've been conditioned to tidy up after men.
In the case of Carol, Louise, and Hannah's murderer (I will not name him, #sayhername instead), he turned those beliefs up to 11 and took them to the conclusion that Louise and her female relatives must be punished with death and, in Louise's case, rape, for denying him what he perceives as his right. I suspect that his motive for denying rape is that in his mind, he's entitled to put his dick in what he perceives to be "his woman" and therefore in his mind, he's done nothing wrong. Remember that a key "teaching" of Andrew Tate is that women don't have rights over our own bodies and hence rape cannot exist because women don't have a right to not consent.
Clearly, he knows that other people don't think like that about women, because he faked niceness when Carol answered the door to him.
That he is a coward who fears other men is clear, through the care he took to ensure that John Hunt would not be at home and his suicide attempt to avoid the natural consequences of being incarcerated alongside other men, some of whom will take a dim view of killing women.
How can someone have this level of white hot revenge drive and been under the radar thus far
Louise may have been the first woman to ever tell him "it's over".