"Do you want black tea?"
Translation:Chcete černý čaj?
I now see it was tea not coffee, so that could have been why the answer wasn't accepted :D. "Daš si černý čaj?" would have probably been accepted.
I don't understand why "Daš si černou kávu?" isn't accepted as a correct answer. As far as I understood from my Czech teacher and friends, they do not use "chtít" when asking about food or drink.
I believe it is common to use "chtěl bych" = "I would like" when talking about food & drink. Maybe your teacher meant only that it is more polite to say "would like" than to say "want".