Reply #14: Under the law in effect at that time, his mother couldn't convey citizenship.

[Jim Lane]

A child with one citizen and one non-citizen parent, if born outside the United States, would be a citizen at birth only if the U.S. citizen parent had lived in the U.S. for at least five years after reaching the age of 14. Therefore, the citizen parent had to be at least 19 years old. Ann Dunham was still only 18 when she gave birth to her son, Barack Obama. Therefore, IF she had for some inexplicable reason flown halfway around the world to give birth in Kenya, far from friends and family, instead of in the excellent medical facilities in Honolulu, then her son would not have been a citizen at birth.

The law has since been changed but the change wasn't retroactive.