Like mm1970, my husband and I have had pretty long dry spells during pregnancy and the postpartum period. In that case, there was a distinct hormonal reason, and the lack of sleep didn't help. I kind of relate to the OP's partner's reaction to the OP, since I have also responded negatively to being touched. In my circumstance, it was having young children in my arms and being manhandled by them all day. It was not fair, but in my mind I just thought of sex and intimacy as one more thing on my "to do" list, as another person who wanted something from me. I have learned, of course, not to think this way. I love my husband deeply. I am still attracted to him. There is no one else I would want to be with. It would break my heart if he wanted to divorce me because we weren't having sex as frequently as he wanted. Honestly it would lead me to step up more. If she doesn't when "threatened" (I don't actually think it's a threat) with the relationship ending, then I do think it is best to end it. Plus you two are still not married and don't have kids. These matters will likely make things much harder.
I'm interested in the idea that a marriage is defined as "sexless" if you only have sex 10 times a year.
I would agree with those who have mentioned the problems surrounding hormonal birth control. I was on it for only a year, and let me tell you - it really did its job. I never felt like having sex anyway. I was an asexual being. It sucked that this was our first year of marriage. The same happened to me on antidepressants. I decided then and there that I had to find a way to regulate my depression without pills.
I want to mention one more thing. Before I had children, sex was oftentimes painful for me. I went to a gynecologist to explore why but never really got a reason. After my first, I was amazed at how much nicer sex was. I'm certainly not saying, "Go ahead and have kids and then see how your sex life is....." I just wanted to point out that sexuality is often very complicated.
What about orgasms and masturbation? I ask mainly to bring out the fact that she might not have discovered her sexuality yet. Some women can be late bloomers in that department. Without this, they might just think of sex as a chore or a service to their partner rather than a mutually pleasurable experience. I.e. when you have had sex, was the sex good? For you? For her?
Ultimately, it sounds like you have made the decision. I also couldn't be with someone who rejected hugs and kisses. It also sounds like she hasn't explained to you why. All this rejection and lack of knowledge must really be painful for you. You really have my sympathies.
Having said that, just because one's sex life is good doesn't mean that one's relationship is. If I had to choose between a good sex life and a good marriage, I would choose the latter. Not saying they are mutually exclusive, but one does not equal the other, despite what people have said. In another marriage thread, I had written about my present struggles with sex frequency, and one regular commenter said that my husband was "thinking of divorce and probably surfing porn." I'm glad to see more varied views on here. Ykphil, you are awesome.