"A academia"

Translation: The academy

[jkazor]

I always thought "academia" means "gymnasium". I am not sure why that is a wrong answer

[Davu]

Just because it was rejected doesn't mean it's wrong (first rule of Duolingo!). Duolingo's own hints suggest "gym" and that's just a shortened version of "gymnasium". See:

http://www.priberam.pt/dlpo/default.aspx?pal=academia