I am not a native German speaker, so I need to explain this in English:
Because the negation should always follow the direct object if the direct object is precded by a personal pronoun.
So because we have "unsere" as the personal pronoun and "Sprache" as the direct object, it needs to come after that direct object, just like it shows in DuoLingo:
Er spricht unsere Sprache nicht.
Das ist der Grund :-)
"Er spricht nicht unsere Sprache" geht leider nicht.