Maybe you don't want to feel exposed or maybe you are not so sure about showing yourself, because you believe that all that really matters is your professional skills. Well, people also want to know you, because they need to know what kind of person they are going to work with.

To me it may say two things about you: you are a person who keeps a lot of secrets and that might be good, because you can be trustworthy, but it also could mean that you have done some things you don't want the world to know about. And it could also tell me that you are very shy, that you don't open up so easily, maybe because you're insecure.

The answer... You only know. In my experience, the only way to deal with such things is confronting them, overcoming your fears and showing yourself that you can. Try on more interviews, maybe on the phone. No matter how erratically you answer, you'll know it's a test, you know it won't matter if you mess up, put yourself in more of these situations, but consciously, so you don't fear failure, but rather enjoy it. You can take it with the joy of a kid playing and you will maybe eventually laugh at yourself. And this will maybe take all the stress away.

Believe in yourself, there is nothing you can't do. My best wishes!