Ahhh, I'm going to give a different answer than everyone here. I fully expect this will be downvoted but I think what I have to say is important.
I think you are taking this way too personally. I will use the example of myself. I have a very severe anxiety disorder and I have suffered a lot with it. I don't know how much of it came from genetics and how much from my environment, but I do know that many people in my family have a variety of mental illnesses. Also even if you try your best to provide a good environment, you can't account for every accident or random happening and the child could still have something traumatizing happing, triggering major mental illness in them where it wouldn't in others.
So I would understand if someone was afraid to have my children because they didn't want the children to inherit my anxiety disorder and suffer. I MYSELF am really really scared about having children for that reason. I would love to have a family but I don't want any children to suffer the way I have suffered.
I have been directly rejected for my anxiety disorder PLENTY of times and dumped because of it.
However, if someone didn't want to have my children because of it, I wouldn't see it as a rejection of me whatsoever. If the person really loved me a lot, and really sympathized with the pain I have been through, then it makes total sense. If we had a child together, they would likely love the child even more than they loved me. It would be horrible to see that child in pain.
To me your situation is the same. You said that your short height caused you great pain. It sounds like your wife really loves you and it upsets her that you were in pain. It sounds like she does not want your future children to be in pain. To me it sounds like she is coming from a place of love rather than a place of rejection.
One potential thing I think you could try is to really delve into the time in your life when you were in pain due to your height. And talk about things that really would have helped and would have enabled you to avoid the pain. If you both could get to a place where you can see that you could have avoided the pain of your younger years, if circumstances or actions in your life had been different, then I think it might help your wife be less worried. A few things that spring to mind are if you had been involved in gymnastics, or horse competitions, which are both areas where short men dominate, and they are usually way more full of girls. Maybe you and your wife could watch the men's gymnastics Olympics in Rio together, which will be full of men your height and shorter who could not have dominated their sport without being that way.