The US rules are not only complicated but they have changed over time, and the determination is usually based on the rules at the time you were born. If both parents are American, or you are born in the US, it is pretty straightforward and mostly always has been. If only one parent is American and you are born overseas, “natural-born” citizenship is not automatic and depends on other factors. Having a single American parent is not sufficient on its own to be a natural-born American under US law.

This is why it became a thing with Obama. If he was born in the US then it was unambiguous. If he was born outside the US then the aggregate circumstances of his birth had a legitimate potential, under the rules at the time, to deem him not “natural-born”. It isn’t terribly surprising that people with a political angle were going to litigate that in the court of public opinion, and the vast majority of Americans have no idea how those citizenship laws work.