When his mother carried him out of the hospital in Calgary, Alberta she was carrying out a Canadian citizen with a Canadian birth certificate.
He was a Canadian at birth — not an American at birth.
http://www.foreignborn.com/visas_imm/start_here/4birth_abroad.htm
He was an American citizen at birth.
The American consulate in Calgary would dispute your assertion.
He was both:
“The following shall be nationals and citizens of the United States at birth: a person born outside the geographical limits of the United States and its outlying possessions of parents one of whom is an alien, and the other a citizen of the United States who, prior to the birth of such person, was physically present in the United States or its outlying possessions for a period or periods totaling not less than five years, at least two of which were after attaining the age of fourteen;”
http://www.law.cornell.edu/uscode/text/8/1401
Barack Obama is the third president born with dual-citizenship. The first was James Buchanan. His father (James Buchanan) was a citizen of Ireland who immigrated to the United States and was naturalized. Ireland at the time was part of the British Empire. Under the force of “nemo potest exuere patriam,” (“No one can cast off his country”), Buchanan remained a British subject his entire life under British law and bestowed this status to his son at his son’s birth. This is not dissimilar to Barack Obama’s status as a British subject at his own birth. Buchanan would have been a British subject his entire life under British law. Obama also had Kenyan citizenship until age 23.
The second was Chester Alan Arthur. Arthur, like Buchanan, was the son of an Irish immigrant (William Arthur). Like James Buchanan’s father, Arthur’s was also naturalized when his son Chester was 14. As was the case with Buchanan, Arthur was also a British subject under British law. Unlike Buchanan, Arthur’s British nationality was rescinded with the passage of the Naturalization Act, 33 &34 Vict. c. 14 in 1870 (at age 41).
And of course our first seven Presidents were born as British subjects but grandfathered in as U.S, citizens under Article 2, Section 1.