I want to date my best friends sister but I don't want to hurt our friendship.
Do you think your friend would be unhappy if you dated his sister?
I don't really care what he thinks, even if we became enemies.
If you are serious about wanting to date your friend's sister, then you should talk to your friend so you don't offend or hurt him. If he isn't ok with you dating his sister, then you have to decide if it will be worth it or not.
I don't want be friends with him anymore.
It sounds like you're conflicted about whether you care about what your friend thinks. I think it's important to take his feelings into account, although you don't have to ignore your own feelings either.