> there not situations where they have to give up citizenship to their country of origin?

One such a case is China. If a Chinese citizen gets the passport of another country they lose their original Chinese citizenship (if China knows about the new passport.)

I wonder what happens if they are born in countries like the USA that give citizenship at birth. Do they have to forfeit one of the two citizenships? And when, at birth by decision of the parents or later on by their choice?