No child can lose US citizenship by the actions of their parents. See:
http://supreme.justia.com/cases/federal/us/307/325/case.html
It takes a lot of work, even as an adult, to lose US citizenship. Barry spending a few years in Indonesia as a kid does not, in any way, rob him of full US citizenship.
Unfortunately there’s no evidence that Obama ever had U.S. citizenship to lose. And under WKA, his parents did not meet the subject clause requirements. Quit trying to confuse people with your ignorance.
You quoted Perkins v Elg and stated a parent cannot renounce the citizenship of a child. In this case, Elg’s father renounced his U.S. Citizenship after returning to his native country of Sweden.
After turning the age of majority, Elg requested a U.S. passport as a U.S. Citizen and received one. She returned to the U.S. and lived as a U.S Citizen. Later, she was denied a U.S. passport upon renewal application because the SoS had determined she was no longer a U.S. Citizen.
SCOTUS ruled the father’s renouncement of his U.S. Citizenship did not have effect on his child while she lived with him in Sweden. The U.S. SoS did not allege Elg was a dual citizen. Elg never claimed to be a citizen of Sweden. Elg could have been stateless if the SoS’s actions were upheld. Consequently, she maintained her U.S. Citizenship.
In Obama’s case, as with Terrazas, he was born in the U.S. with one U.S. Citizen parent and one foreign national parent. Both Obama and Terrazas were dual citizens at birth. All dual citizens are a risk of Loss of Nationality if they move out of the U.S. and participate in acts deemed to have renounced their U.S. Citizenship by a preponderance of the evidence as determined by the Secretary of State.
As opposed to Elg, where the SoS did not establish Elg was a dual citizen, the SoS did determine Terrazas and Obama were citizens of another country before the Certificate of Loss of Nationality was issued.