It sounds as if your boyfriend needs to grow up and accept responsibility instead of denying it. By not allowing you to tell anyone he's trying to hide from it.
Maybe he'll come to accept the baby, maybe not.
You describe your relationship as "good." I'd expect you to use a stronger term to describe the relationship. Is it really "good" or are you both just "comfortable" in the relationship? Does he now feel "trapped" and unable to leave?
Counseling might be an option, for both of you.
As a divorced mother, I have a different opinion about this. So many of my friends have gotten into custody battles and come out with less than ideal outcomes that I think... if he wants to bail now and never come back, that might give your child more stability than if he keeps popping in and out of the child's life. Having relationship problems while being pregnant is also really difficult. It ups your stress levels, which can affect the baby.
I think you should talk this out honestly and decide what to do from there. If he wants out, better now than later on.