All true. But in addition, we really don’t know if Obama IS a citizen. He may still have Kenyan, British, or Indonesian citizenship.
Since there is no evidence that he ever took the steps to get his American citizenship back after his parents relinquished it in Indonesia, he may be an illegal alien.
There's been discussion about whether or not you have to assert your rights in some manner if that happened. Most of the claims that you have to assert it involve kids coming back to the US from Mexico ~ and there their parents didn't need to do anything to turn them into Mexican citizens.
The laws are highly complex and are NOT equal for everyone. That's because the immigration codes are written primarily for foreigners, and though they have some rights under our Constitution (like, we don't kill'em and stuff them in sausages when their visas expire) they are not considered equal in rights to a citizen, and each country's nationals can have different treaty rights or requirements.
Your parents can NOT relinquish your citizenship for you. NO ONE ELSE CAN either. Only you can relinquish your own citizenship AFTER the age of majority.