"I am his younger brother."
Hah, I answered the same. It counted me wrong, but I'm gonna report it, because I don't think it's GRAMMATICALLY incorrect. It just emphasizes who the younger brother is.
"Man, that guy is so cool!"
"Yeah, and I heard he has a younger brother in our grade."
steps out from the shadows after eavesdropping, striking a Dramatic Anime Guy pose "His younger brother is ME."
Correct me if I'm wrong, but to me this seems like it would be translated to "Speaking of his younger brother: that's me, by the way." If 僕 and 私 can be used like that (which I don't know), it would be useful in a conversation where e.g. the younger brother just enters while his older brother is talking about him, but I can't think of any usual situations where you would say it like that. :)
It is grammatically correct, but it is not correct because the topic is different. To make sense about this, try finding questions which have these sentences as answer. In these cases:
A: 僕は彼の弟です。(I am his younger brother.) Q: あなたは誰ですか? (Who are you?)
A: 彼の弟は僕です。(His younger brother is me.) Q: 彼の弟は誰ですか? (Who is his younger brother?)
Yeah, the second structure is like saying "His I am younger brother". It's difficult to explain, but it's how a sentence is structured in Japanese. Usually the subject (if it's mentioned; in this case, "watashi"), will be in the start of the sentence. Another thing is that "kare no" and "otouto" should be together because "kare no" is working as the possessive case that indicates that it's not someone else's brother, but his brother.
So you're implying it was marked as wrong? Because it actually should be, you're right. In any situation that I can think of, it should be clear from context what you're saying. Though, I could imagine that Duolingo got a problem with you writing that in hiragana, as I've read in these comments that it's rather unusual to include the お, unless you take the kanji, as the kanji includes the o by itself. I did not exactly get that myself, but I would recommend just using the kanji whenever possible, as that is one of Duo's strong points: It always prefers kanji, as Native Japanese people would do.
This is how Japanese generally works. As long as your particles are correct and your verb is at the end, you can put your sentence in whatever order you want for the most part. The rule you want would have to be made up for Duolingo, and there's really no reason to do that.
Unless I misunderstood and you are being sarcastic?
I believe the correct structure you are looking for would be "kare no otouto, watashi wa" (his younger brother, I am) even though that sounds a little animeish and would be rather weird. The most natural structure would be "watashi wa kare no otouto desu".
By saying what you quoted, It'd sound like "his I am little brother", and that grammatical structure sounds wrong to me. Maybe Duo doesn't accept it because it is not acceptable.
Note that the suggested answer by Duo is "Boku wa kare no otouto desu", that is because Duo wants you to note that boku is more masculine than watashi, and also that otouto is a younger sibling than the speaker and that is a male.
Without the です in this case would be (non-past tense, affirmative) short form. It's used in certain grammatical patterns such as quoting others ([someone]は[quote in short form]と言っていました = [someone] said [quote in short form]). It's also used in casual conversation, as you mentioned, at the end of the sentence (as well as in the aforementioned grammatical patterns). So you could say that to a friend or a family member, for example, or someone beneath you in rank like if you were a teacher talking to a student. But you couldn't use it in polite conversation, like a student talking to a teacher, or with a stranger. In those polite cases, you'd have to use "long form" or the polite conjugation, which would include です in this sentence.
If I'm not wrong, or leaving something out... I believe it's something like this:
Masculine: 僕（ぼく） Is used men and young boys. Common. 俺 （おれ）Is used by men and can be rude at times.
Feminine: 私（あたし）Is a common way of saying "I". 内 （うち） Is sometimes used by young girls
Gender-less/Used for either: 私 （わたくし）More polite/humble (Not really used for everyday - more for those in the service industry or business situations.) 私 （わたし）Common so safe to use.
They carry different connotations, but both refer to oneself. "Watashi" is the most neutral, and very commonly used by men and women. "Boku" carries a boyish connotation (used by tomboys, boys, and sometimes boyish men. Also, because of its syllables, it is often used in songwriting.)
の in this sentence indicates possession. In the given answer, the phrase "彼の弟" is equivalent to "his little brother." In your sentence, "彼の僕" would be something like "his me."
As for が, I am a bit more uncertain of this, but I think it's used basically in place of は when you are adding a new topic or new information/sharing information that is not common between the speaker and listener. It could be correct in this sentence depending on the context.
There are many ways to refer to oneself. "boku" is boy-ish in connotation, "ore" is self-important in connotation (but can be used in a joking/sarcastic way -- kind of like referring to yourself as "my wonderful self" around your friends), and both refer to oneself. The possessive form is (word that refers to oneself) + no. So, "bokuno" or "watashino" and so on.
But I saw a video by a native speaker saying that foreign men should use "ore". She even said she doesn't like guys that use "boku" because it's used by young boys and has a "momma's boy vibe", paraphrasing. I feel like there's mixed information on how or whether to use "ore".
Maybe she just likes guys who talk themselves up? What I described above is what seems to be the case after hearing various natives' take on it. Several said it shouldn't be used at all, but the one who was giving me more data points than opinion explained the connotation behind it: "my wonderful self." Besides, since it's used in anime a lot, you have to worry about foreigners using it a lot, too, since people may think "oh, that foreigner is just copying anime." Personally, I think "watashi" is the best one to use, since it's neutral and gives off a polite feeling. Of course, you should refer to yourself with the connotation you want to give off. Like, a tomboy may want to use "boku" to make herself sound more rough and tumble, but a frilly girl may want to use "atashi" to match her style. And if you're a guy trying to come off as tough, maybe use "ore." But, really, especially if you're a foreigner living in Japan, you're going to want to be on your best behavior, since it's easy for native Japanese to have a mindset of "if anything goes wrong it's because of those foreigners." Not all of them think this way, of course, but you fellow foreigners won't be too happy with you making life harder for them because of that stigma. Basically, just like anywhere, it's important to consider not only how you want to be seen, but the resulting effects of how others see you. Decide how you want to present yourself based on all the inherent pros and cons, and do your best to figure out what this action or that action will lead to. What kind of impression do you want to make? That kind of thing.
It changes it to "His younger brother is me.", which kind of says the same thing, so it should be mostly fine in general, but it does shifts the focus.
僕は彼の弟です "I am his younger brother." would feel more approriate when you are making statements about yourself.
彼の弟は僕です "His younger brother is me." would be more approriate as an answer when someone asked about who his younger brother is.
僕 = I (masculine)
は = topic marker - in this sentence it basically indicates that what precedes it (僕) is the subject.
彼 = he
の = possession (in this sentence. It can also add information to nouns)
弟 = little brother
です = is/am (present and future conjugation of to be)
僕は = I (topic)
彼の弟 = his little brother
です = am
僕は彼の弟です = I am his little brother
Hope this helps.