Translation:No, that's incorrect.
That's a fair point. Politeness does also depend on nonverbal communication though, such as tone of voice, as well as the context. I agree that "you're wrong" generally sounds less polite, but I think "that is wrong" or even "that is incorrect" would sound on par, or close enough, if said with the same tone of voice, etc.
I love Danganronpa, it's just so over the top XD By the way, "dangan" (弾丸) means "bullet" and "ronpa" (論破, written in the background) means "refutation", so "danganronpa" literally means "bullet refutation". That's a reference to the game mechanics, in which you refute arguments using "verbal bullets" (コトダマ - kotodama)
You're right that 違う also means "to differ", and in a sense, the idea of "wrongness" comes from being different from the correct answer.
However, although I think "it's not that" should be accepted, it's almost too literal. 違う is used in Japanese specifically to capture the sense of "wrongness", without outright saying someone is wrong (remember, Japanese people tend to avoid saying things too straight, lest they risk offending somebody).
Have a read of my comment on b's post. I think much of what I said applies to your suggested answer too.
That being said, Duo isn't necessarily mistaken, but it's just a natural outcome of a translation-based learning system like Duo's. "It isn't" is probably associated with some other phrases in Duo's database, so when it compares your answer to the exercise's ちがいます, it says you gave the wrong answer. The course creators haven't thought of every possible situation this sentence can be used it, so they just haven't included every possible variation of the correct answer.
This explains it well :http://www.punipunijapan.com/japanese-particles-yo-ne/
Unfortunately, I would say it was the latter. There's nothing in the Japanese sentence that specifically says "that", so "this" is an equally valid translation (in the absence of any other context, as this exercise is).
I suggest flagging your answer as correct for the course developers to fix/add to the pool of accepted answers.
Please try to read the other comments first; your question has been answered numerous times already.
違います is a verb which means "to be wrong"/"to differ", so if something is wrong, it's a positive. For whatever reason, Duo's course developers decided to teach it as "is not right" (which is synonymous with "is wrong").
Oh, my apologies. I guess I was misremembering, perhaps mixing this page up with the English -> Japanese version of this question. I could have sworn I've answered questions similar to yours myself at least 3 or 4 times before.
I'm sorry for my curt tone, but I hope you can understand how frustrating it can be sometimes to carefully craft an explanation, only to find people aren't bothering to read it. I was wrong to assume that's what happened this time, but it happens a lot in these forums.
So why all of a sudden can I not see the hiragana or katakana characters anymore? Sometimes they're question or exclamation marks. Everything would display properly before, what's happened?
違う is a verb that means "to differ or to vary". 違い is a noun that means "difference or discrepancy".
違います is the polite form of the verb. 違いです is the noun + polite copula.
So if you want to say "It is a discrepancy", you would use 違いです, but if you want to say "it differs" you say 違います (or 違う).
The verb is used pretty frequently when you want to let someone know that they are wrong or mistaken about something.