Obama’s listed father is not an American citizen. The child takes the citizenship of the father! Furthermore, both parents must be citizens. Obama may be a citizen but he is not a ‘natural-born citizen’!
§ 212. Citizens and natives.
The citizens are the members of the civil society: bound to this society by certain duties, and subject to its authority, they equally participate in its advantages. The natives, or natural-born citizens, are those born in the country, of parents who are citizens. As the society cannot exist and perpetuate itself otherwise than by the children of the citizens, those children naturally follow the condition of their fathers, and succeed to all their rights. . . .
Emmerich de Vattel, The Law of Nations
This is the definition, and intent, that was used by the Founding Fathers when they scribed the US Constitution.
Natural-born citizens of the United States are those who are citizens of the United States from birth without having to perform any act to acquire or perfect their American citizenship. These are those whose parents are citizens of the United States at the time of their birth.
Natural-born American citizens are those born of American citizen parents,within or without the American Republic, provided in the latter case that one of the parents had resided in the United States prior to the birth of the child.
Their American citizenship is natural, the result of parentage, and not artificial or acquired by compliance with legislative provisions.
A natural-born citizen is one not made by law or otherwise, but born. And this class is the large majority, in fact, the mass of our citizens; all others are exceptions specially provided for by law.
A natural-born citizen is defined as one whose citizenship is established by the jurisdiction which the United States already has over the parents of the child,not what is thereafter acquired by choice of residence in this country.
It is not necessary that a man should be born in this country, to be "a natural born citizen." It is only requisite he should be a citizen by birth, and that is the case with all the children of citizens who have ever resided in this country,though born in a foreign country.
Natural-born citizens, as distinguished from aliens and naturalized citizens, are those born in the United States of parents who are citizens.
Natural-born citizens are also those born outside the United States and its outlying possessions of parents both of whom are citizens of the United States and one of whom has had a residence in the United States or one of its outlying possessions prior to the birth of the child.
Hence, a child born abroad to two US citizen parents is a natural-born citizen:Provided, That at least one citizen parent had previously resided in the United States or one of its outlying possessions. U.S. Code: Title 8, 1401.