If the father, for example, was born in Switzerland and he married an American woman, I believe he should have the right, assuming his wife agrees with it, to have his children in his original country. This way they could be in touch with the culture their father grew up with, and they can be able to see the world. I don't see anything wrong with children being born in different countries and having citizen ship in two countries where their parents were from, so long as they remain with their families and can stick with them and eventually know just why their parents opted for that.
Shadowhunter’s reply fails to take into account that many nations already offer citizenship to the children of their citizens, regardless of where they were born. Thus, in his example, a Swiss man could marry an American woman, and have their child in Australia, gaining it citizenship in all three countries. This has been a background feature of several Canadian lawsuits. In one, an illegal Jamaican immigrant claimed compassionate reasons to allow her to maintain residency rather than being deported because her children were Canadian citizens — due not to the citizenship of their parents, but rather, purely by virtue of their being born in Canada. This is clearly an abuse of the system and extending automatic citizenship to anyone born within a country’s borders merely opens them up to that abuse.
The point of citizenship is being a citizen. Why do you think countries don't like dual citizenship? It creates a society where individuals have two loyalties and you can't serve two masters. And also if the father or mother DECIDED to come to a different country to live and raise their children don't you think that is a bit selfish to say your kid is from Switzerland but to raise him in another (most likely richer) country?