Why is my brother so embarrassed about this?

He might be ashamed because maybe he was hoping to hang out with his new wife before a baby came. If he's that set with being embarrassed then there's nothing you can say to help him feel better. Its going to take him coming to terms with his finance's pregnancy to finally be o.k with the situation and be happy. Its only the first trimester, he hasn't had time to process all those emotions. Give him time and some space, don't nag and hound him. He'll come around eventually, that baby's gotta come out someday!