Why isn't Obama's Certificate of Live Birth enough to prove that he was born in the US?

I'm having a discussion with a very conservative family about the nature of Obama's citizenship. Despite the numerous links I have found from various sources confirming his US Citizenship, they still claim that no one can be sure without having seen his long-form Birth Certificate. To my understanding, the... show more I'm having a discussion with a very conservative family about the nature of Obama's citizenship. Despite the numerous links I have found from various sources confirming his US Citizenship, they still claim that no one can be sure without having seen his long-form Birth Certificate. To my understanding, the Certificate of Live Birth carries just as much legal weight as the long-form birth certificate, so why does doubt remain? Donald Trump has unburied this controversy and I want to be sure of the facts.
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