A factoid about Anthony Burgess and ACWO: "After doctors found a cancerous tumor in his brain, he wrote "A Clockwork Orange" in a hurry, hoping that the money made from the book would support his wife after he died. He later found out that he did not have cancer."
"Друг" - is used with a masculine friend;
"Подруга" - is used with a feminine friend. But if a boy calls a girl "подруга" it has a dual meaning - in one case it means that she is his friend, in another his girlfriend.
"Ты мне не друг" (you are not friend of mine) means in Russian "you don't have friendly relations with this person and you don't want to have it", "communicate with me formally only, I don't want to talk friendly with you" or "I don't want to communicate with you at all". This sentence can be used also to say someone a phrase "you are a stranger to me", when you want to say "stay out of my life".
"Ты не мой друг" / "ты не моя подруга" (you are not my friend) - this is another sentence with a different meaning in Russian - "you don't have friendly relations with this person", "you are not my friend, but you are a friend of another person". This sentence can be used also to describe a situation"stay out of my life" if one would say this phrase with anger. Thus, the last sentence depends on the context and the intonation (edgy, etc.)
It is exactly the same in English. "You are no friend of mine" is definitely saying "I dislike you, I do not wish to be friends with you". "You are not my friend", without some context to make it stronger, is just a statement of fact (although it's hard to imagine a situation in which it would be truly neutral and not a bit insulting).
Odd that Duo has not introduced the word "подруга" yet.
In English, "girlfriend" has undergone a slight expansion in meaning recently. As a standard starting point, when a male mentions "his girlfriend", he means a female with whom he has some sort of romantic attachment. A female friend is "a female friend" a "a friend", not a "girlfriend".
Between women, a "girlfriend" can be either just a friend who is female or a romantic relationship. Some gay men use the word in a similar way to talk about other men or women.
It is not a good translation, so Duo was right to mark you wrong.
"a good friend" = хороший друг, and хороший isn't in the exercise sentence.
Also, the concept of "no friend" = the complete absence of a relationship is very different from "not a good friend" = a poor relationship, but a relationship none the less. Absence vs. presence.