Proof he didn’t?
Let’s see - his Mom filed for divorce in Hawaii. I doubt she would be able to file for divorce in Hawaii if she & her husband were born foreign citizens.
Further, Barry returned to the US permanently at the age of 10. Even if he had done so on an Indonesian passport, by living here since then, he has claimed what country he wishes to be a citizen of - and that would be the USA. He could NOT lose his US citizenship (if he was born in Hawaii) by living in Indonesia for 4 years, nor by applying for citizenship there (no evidence), nor by filing paperwork no one has seen renouncing his citizenship at the age of 6!
Perkins V Elg. Elg was born in the US, was taken to Sweden at the age of 4, by treaty became a Swedish citizen 2 years later, and didn’t make any attempt to return until just prior to her 21st birthday - and the Court ruled she was still a citizen.
Your “arguments” have been disproved countless times.
Snicker.