Sex in most relationships is pretty important, particularly in the beginning of a relationship when you're getting to know each other, that means mentally, emotionally and physically.
It is OK to not want or enjoy sex, everybody is different. I could be wrong but I feel that given your aversion to physicality in relationships, your use of "demanding sex" is perhaps a little unreasonable, however it is unrealistic to think that most people in the early stages of dating and establishing relationships don't expect/want it. Anyone that DEMANDS sex, is not right for you, nobody has the rights to your body but you.
If its too personal and you don't want to answer that's totally fine and I am sorry for prying, but can I ask why you are against sex? Is it a genuine lack of interest, fear of sharing your body intimately with somebody else or generally finding the idea of it unpleasant? I truly hope you haven't had any sex related trauma and if you had, you are getting/able to get help with that.
There are plenty of asexual people, and I haven't looked myself but I would be surprised if there aren't dating sites for asexual people who want romance and intimacy without a sexual aspect. Intimacy isn't all about sex either.
I can near guarantee that you will not be single forever and there are plenty of people out there that want just what you do.
I wish you well, you'll be alright x