“Obama is hiding his original birth certificate because it probably lists his birth name as “Barry Dunham”. Since Obama, Sr. was already married in Kenya and bigamy is illegal in the U.S., the birth certificate may have even listed Stanley Ann Dunham as “Single”.”
His mother filled for divorce from Obama Sr. The divorce papers are public record. She was married to him.
Another point is that if BHO and SAD were married at the time she gave birth - as the HDOH records seem to indicate -the BC would automatically list BHO as the father. If they weren’t married when Obama was born they could get the BC changed to say that they were through the process of legitimation.
Obama’s lawyers have talked about the potential embarrassment but there is nothing on the COLB especially (which he and the HDOH refuse to release - even a non-certified copy which is required to be public upon request) which would “embarrass” Obama unless it exposed his ineligibility or that he’s been lying about his history all along. All the typically “embarrassing” scenarios like illegitimacy, sex change, etc can be hidden legally without any amendment involved because a new BC is created and swapped out for the “embarrassing” one, which is then sealed and can only be opened by a court order.