This sounds abusive, really. I'd buy this fight and avoid him until you can be completely apart.

I can't help but think of the opposite situation. I never see a man being 'demanded' to have sex in similar settings. It angers me a bit that sex pops here and there as a duty in a woman's life, even when she doesn't want it or isn't trying to pursue a specific man anymore.

If you agreed with living under the same roof but not as a couple your relationship should be of roomates. He can't demand sex from you and you can't really get mad at him for getting involved with another woman. I don't know why he did that if he agreed with not pursuing others, though. Maybe you should change the rule so he'll know he's not the only one doing it.
Keeping the house clean and respecting each other is mandatory in any relationship where people live in the same house.