The ETIAS visa waiver was created to gather information on non-EU citizens who could travel to Europe visa-free. Citizens of 60 countries, including the United States, are required to apply for ETIAS before traveling to the Schengen Area. Those that are not eligible for ETIAS are required to apply for another EU-visa like the Schengen visa.
If you have dual citizenship, you can apply for the Etias with either passport as long as the country is eligible for the ETIAS visa waiver program and that the passport is valid for at least 6 months at the time of the application. Also, keep in mind that travelers are required to travel with the passport they used on their ETIAS application. Which means you will have to travel with the passport that is directly linked to your application.