No? If you're born in the US you have US citizenship, you're American. You don't just magically get citizenship for your parents home country, at least not for most countries.
Also, in some cases, you may automatically lose your original nationality if you seek an additional one (Spain comes to mind; though in their case you'd need to manually request not to lose your nationality to keep it within a certain time period, IIRC).
> You don't just magically get citizenship for your parents home country, at least not for most countries.
Are there any countries where this is not true? I struggle to think of any, especially amoung highly-developed democratic nations. (There might be a couple of weirdo dictatorships that do not allow it.) It seems this would be necessary to prevent statelessness. For example, if your parents are living in the Netherlands as foreigners, children born there are not entitled to automatic Dutch citizenship. As a result, they will obtain citizenship through their parents (in a foreign nation).Most countries determine citizenship eligibility primarily by parentage, not place of birth.
The whole concept of getting citizenship where you're born is mostly an American concept. Though, if you do get born in a place where you get citizenship based on location alone, your parents will probably need to figure out a lot of paperwork to sort things out.
You can automatically be a citizen through descent of most countries in Europe and Asia, and everywhere in North America.
https://en.wikipedia.org/wiki/Jus_sanguinis#Jus_sanguinis_st...