Is it that he doesn't want a cat enclosure at all, or he doesn't want to help do it??

It kind of sounds like he doesn't agree with having one at all. And if you're living with your parents, you have to live by their rules - they pay the house payment after all.

Maybe you could make something smaller and temporary you can set up on the warm weekends or something? Then he can see what your goal is and understand why you want your kitties to have one.

Are your kitties indoor only?