Buchanan’s father (also named James Buchanan) was a citizen of Ireland who had immigrated to the United States and became naturalized as an American citizen.
The information not supplied here is important. Buchanan's father immigrated to the colonies in 1783 and when the Constitution was adopted (1787) all residents of the United States had citizenship (Naturalization) conferred upon them immediately. James was born four years later in 1791 to a now recognized by "Naturalization Law" American Citizen. So.....James was born of the soil and born of the blood.....a "Natural Born Citizen".
What exactly is it about this apparently difficult (for you) scenario that you don't understand?
As I said, it was the operation of BRITISH law that made both of the Buchanans British citizens for life as well as American citizens, the father naturalized and the son a Citizen of the United States at Birth.
What part of “Nemo potest exuere patriam” meaning “No one can cast off his country” didn’t you understand?