> 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).
Quite a few countries do not allow dual citizenship. So a person who was born in the US and is therefore US citizen at birth will not be allowed to have that country's citizenship until they revoke the US one.
China and Singapore are some of the more prominent examples.