"My big brother is tall."
It's correct, too. Because of the の nominifier,「兄の背が高い」 literally translates to "My brother who is tall" or "My tall brother". It makes that adjective something your brother owns.
But Duolingo wants to express a subject and a complete sentence with the use of は. And, in that sentence, you see an 'ownership' of that brother of yours (whom you say is tall) because of the の nominifier.