I've never quite understood this notion of someone being born in America becoming a citizen, even if neither of the parents are citizens. Where did it come from?
It comes from English common law. According to English law, the nationality of the parents was irrelevant; all that mattered was where the child was born. Anyone born inside England was considered a subject of the king, even if the parents were aliens. Similarly, anyone born outside England was considered an alien, even if his parents were English.
(It is true, there were a few narrow exceptions to this general rule; for example: the children of diplomats.)
And... why was that the case?
I'm looking for a justification, not just vacuous precedent.