The nation must not be understood to be identical to the state. A state is a system; it is composed of artifices, of laws, the products of the human mind. A nation is a people, and a people may have one state, or multiple states, which may change dramatically over time. Remember the Indian tribes, which were often organized into autonomous bands, or the classical Greek city-states. There were regional variations, of course, but there was an awareness of people-hood, or nationhood, that set them apart from others in the world.
Consider the analogy of the family; the family is a natural, organic entity. It is lived and experienced, and membership in the family is dictated by shared experience. There are, of course, deaths and births, and adoption may occur, but the reality of the family is never in doubt. A family, too, may be said to be governed in various ways; the management of household affairs may fall on the woman, and the family may respect the headship of the father. Perhaps, in times of necessity or for other reasons, children may be sent elsewhere, e.g., to be educated or cared for, but the basic integrity of the family remains.
Dual citizenship might be possible on a piece of paper, but it is impossible to have two mothers in the full sense of the word and really fully belong to both. You can claim citizenship under two, three, or four states, but claiming several nations is as absurd as claiming to have four mothers! The minute you call yourself both Mexican and American, or both Chinese and American, I know you are not one of my kind at all, even if you have the right passport. You may have been raised here, you may drink the same water, read the same books, but you have already decided that you are something else, something "additional" to my brother.