You will NOT logic your way out of this.
what caused this is emotional, and there is ZERO amount of anything you can do with words to solve this. She made an emotional decision, and is using her religion as a means to rationalize it.
It will NOT matter how logical your point is. She will continue to make emotional decisions, without your input, and then rationalize them.
Any attempt to use logic with her would at the very best only result in her doing a few little sexual things with you, and even then should we act like she hates it while she’s doing it and as if she were being abused by a gross pervert. – That would be very degrading. And that is the BEST case scenario.
More likely she would get explosively emotional at your attempt at real logic and then use her rationalizations to VILLIFY you. Likely talk to all her friends about what a "bad guy" you are. – Even though you’ve been going out of your way for her, and she seems to not appreciate it at all.
Again, no amount of logic will correct this.
Ask yourself some questions; What are you afraid of if leaving her? Are you afraid of being lonely? Are you afraid of people shaming you for leaving her?
Perhaps her extreme emotional tantrum when you dump her? When she shrieks about you doing it because you’re a "BAD GUY man, icky male, who only wants seeeeeex, because he’s wicked and evil with his evil peeeenis!" ?– when she does this, don’t try to "logic" her out of her rage.
This only adds fuel to the fire. One cannot logic that which behaves and thinks illogically.
If you live with her, get all your important stuff out of the shared place. Contact family, friends, someone you can stay with until you are back on your feet with your own place. Anything of value, get out of there before dumping her if you can, to avoid the self-righteous rage of "break stuff he owns, because he deserves it for dumping the great and holy and infallible meeeee" that could follow dumping her.
You will get over it. You will find someone new who treats you better and appreciates you. You are NOT a bad guy for breaking up with someone. There is also a LOT more dignity in being alone than having an emotional parasite sucking the life out of you.
Lots of folks will tell you to talk to her. What they are saying is try and get her to see logic. They don't account for what to do when that fails.
Logic has already failed. Trying it again is insane. Don't do the same thing over and over and expect to get a new result. That makes you crazy.
Actions speak louder than words. She’s fired. This is an advice thread, and my advise is to dump her.