"American" would be ambiguous in this context, right? Both the Cherokee and the English-speaking residents of the USA are American, but the specific point here was about whether Sequoyah was only a Cherokee speaker or if he had any knowledge of English, Spanish, French, Latin or any other European language. In this context, saying that Sequoyah's father was "American" would not make any point - it wouldn't tell anyone reading the comment that he was not Cherokee nor from any other native population; whereas European makes that point succinctly.