It is weird. Because, every US male tourist out there who fathers a kid creates a US citizen or similar for military personnel fathering kids abroad. Vietnam would be full of US citizens running around because of their ‘fathers’.
You carry your American citizenship with you wherever you go. If an American citizen creates a child in another country, the American citizen can go, if she/he wants to the American Embassy and register that child as an American citizen.
My son married in England to an English woman. They lived in London, child born in London and son went immediately that day to the American Embassy and the son was an American citizen that day and an American Passport for the new American citizen was given to son that very day. He has dual citizenship, American and British.
When the child comes to America, he goes to the American citizen line to come into the country. His mother, being a British citizen, has to go to the out of country line to come into the country.