Cool. A chance to play Cary Tennis. Here is what I think.
The two of you should agree on a period of time for soul searching. Say, a month. During that month, you will honestly consider whether or not you are willing to get married to this woman and have children with her. I know you don’t want to now. But give yourself a month to think about the issue in a concrete fashion – not just “I don’t want kids or to get married,” but “is this person worth sacrificing some of my desires for?”
At the same time, she must spend the same month searching her own soul, honestly considering whether or not she’s willing to stay with you if she has no hope of getting a marriage or children out of the deal. Are you worth sacrificing some of her desires for?
During that month, do not talk to each other about what you’re thinking re: marriage and kids. Enjoy each other. And spend some time reflecting. Seriously. Each of you must be open to the possibility that you might change your mind if this is going to be worth your time.
At the end of your chosen month, go out to dinner somewhere you can have a long conversation. And talk honestly, as you have done, about your feelings. Have you changed your mind? Has she?
If neither of you has changed your mind, discuss what that means for your relationship. Do you end it now? Are you both happy going out for X more months together? Do you date while she also keeps her eyes open for someone else? You know each other better than any of us do, so only you know what the answers to these questions can be.
If, however, she wants to stay together and continue to hope that you’ll change your mind someday, I recommend that you end the relationship. Not for her sake, although she’ll probably also benefit in the long term. End it because you will be miserable in a relationship like that, knowing that you’re not going to change her mind, telling her you won’t change her mind, her hearing you but not really understanding you.
One more thing:
This sounds like a load of self-pitying horseshit, honestly. Of course it matters what you want, or you’d get married and have kids. Be good to yourself, and be good to her, as best you can.