A US citizen is either Naturalized or Natural Born. It is irrelevant where BHO was born. His father was a British Subject, therefore he required 8 USC, Chapter 12 to Naturalize him at birth. A person cannot be both.
That’s one legal theory however nineteen court rulings have said that Obama is a natural born citizen and no court ruling has ever said that he is ineligible.
For example: Purpura & Moran v Obama: New Jersey Administrative Law Judge Jeff S. Masin: “No court, federal, state or administrative, has accepted the challengers’ position that Mr. Obama is not a “natural born Citizen” due to the acknowledged fact that his father was born in Kenya and was a British citizen by virtue of the then applicable British Nationality Act. Nor has the fact that Obama had, or may have had, dual citizenship at the time of his birth and thereafter been held to deny him the status of natural born. It is unnecessary to reinvent the wheel here. … The petitioners’ legal position on this issue, however well intentioned, has no merit in law. Thus, accepting for the point of this issue that Mr. Obama was born in Hawaii, he is a ‘natural born Citizen’ regardless of the status of his father.” April 10, 2012