So, no one else has wanted to ask why we use "kein" here and not "nicht"? I translated correctly from the German (why don't you eat fruit?) but I would have guessed that if you wanted to negate the verb then you should use nicht and if you wanted to say no fruit then you would say kein...so, in this case, can you also say, "Warum isst du Obst nicht?"
Yes, but if you wanted to use 'fruits' in German, it would be better translated as Früchte, which is plural (and has a singular, die Frucht). Frucht is a biological fruit, i.e. something that hangs off a tree and comes from a flower. Obst is similar to the English fruit, meaning apples, pears, berries etc., even if they aren't actual fruits.