The other problem is that if he was not born in Hawaii, but instead Kenya as his relatives there seem to assert, he would normally also be a US born citizen because of his mother’s status.
However, that is not true either because she did not maintain US residency for ten years when she moved to Indonesia. This was the law of the United States at the time.
Barack may have assumed he was a US citizen all his life until he started researching these technicalities.
Indeed, why did he travel to Pakistan in 1981 on an Indonesian passport?
(It was against the law in 1981 for US citizens to travel to Pakistan, btw.)
All this is very very strange.
You've got that slightly confused. The law at the time required that the US Citizen parent have been a resident in the US for at least 10 years prior to the birth, 5 of which had to be after the age of 14. His mother was barely 18 when he was born. If that was in Kenya, he was not a citizen at birth, although eligible for naturalization. Doesn't matter what the parent does or where they live *after* the birth. The requirements are different now, less years are required, but that was the law at the time.