OK, but in English the word Dutch can mean both female and male. The same with other nations. In Polish you say "Polak" for Polish man and "Polka" for Polish woman, but in English for both you can say Pole. Also in other DL exercises, for different languages as well, it is always accepted, that in English you don't have such a strong gender distinction and one word can be used both for male and female. Good example is secretary - in Dutch you say "secretaris" for male and "secretaresse" for female secretary and in an exercise DL accepts translation "secretary" if the word in Dutch is "secretaresse", so I don't know why in this case it is different.
With the difference being that in English there are no separate words for secretaris and secretaresse, while Dutchman (http://www.oxforddictionaries.com/definition/english/Dutchman) and Dutchwoman (http://www.oxforddictionaries.com/definition/english/Dutchwoman) do exist. Plus the Dutch normally refers to the people of the Netherlands collectively.
Perhaps a more obvious example. You also say the Spaniard to refer to a single Spanish person and not the Spanish (and yes in this case English does not have a separate word for a male or female inhabitant of Spain).
OK, I see that for some countries you can use -woman as Frenchwoman etc. Nevertheless, in my opinion both gender specific (Dutchwoman) and general term (Dutch) should be accepted in such situations. The use of "-woman" nouns is quite rare, I think. Honestly, I've never seen it earlier, altough I have been using English for almost 20 years. :)
The fact that you are learning a language forces them to consider the general term Dutch incorrect. It may not be false in general, but here, it is not just a Dutch, it is either a Dutchwoman or a Dutchman. And, in real life, if you have -se in the end, everyone would translate it/consider it as a Dutchwoman, not a generic Dutch. To say Dutch, they would use Nederlander.
Dutchman and Dutchwoman are Duo English words. The only exception is "The Flying Dutchman" which is a specific name of a fictional ship in an opera. Dutch man, Dutch woman are the normal English usages. Reported. The only English nationality concatenations I have found in my dictionary are "Englishman", "Englishwoman", "Frenchman", "Frenchwoman", and "Chinaman" (but not "Chinawoman") (Other dictionaries may vary.)
I understand what they're going for, but I can't say that I've ever heard the word 'Dutchwoman' in my life.
I get the feeling that nationality-as-noun went out of style at some point (at least in the US), as most of my encounters with it have been in novels and older written works. That being said, "Dutch woman" is an acceptable answer, so I can't complain too much.