I'm going to break up with my girlfriend because she won't spend the night
How did you bring that up to her?
I didn't bring it up. I simply left her house
You shouldn't expect your gf to do things she isn't comfortable with. You need to learn to respect her boundaries.
Having sex is a duty between partners.
Not everyone in a relationship wants an intimate component and you pressuring your gf to have sex with you is wrong. If you push her into doing things she isn't ready for, things will go wrong between you quickly.