you know what duolingo??? that is the most confusing word in my liiife! glad i got it correct. hmmp i'm not going to fall from your traps *insert evil laughs hahahaha
you know what... i am going to understand that in the future. hahahaaha i really can't understand what you're saying.
Actually, this one is probably more complicated than you think it is. The second "나" may also be the subject. In this case, the first "나는" would be qualifying the second "나", and the translation would be "I, who is flying, am a man." which is an accepted answer.
Edit: I, who am flying, am a man. In this sentence, "who" replaces "I," therefore, the verbs in the relative and main clauses should be conjugated in first person singular.
Prescriptivism, or descriptivism, that is the question.
Strang 1970 and Copperud 1970, 1980 note that there is conflicting usage with the first person pronoun: "It is I who (is? am?)." Strang points out that in earlier stages of the language such a sentence would have been unmistakably governed by the first person pronoun and would have begun "It am I...." But over the years the position of it caused it to be felt to be the true subject, and the third person verb is replaced am and sometimes governed throughout the sentence. Copperud opines that, strictly speaking, am should follow I, but says that "there is a strong tendency to use is, since am sounds artificial." Copperud's remarks confirm Strang's comment that this conflict is not yet resolved. (Webster's Dictionary of English Usage, p. 565)
Both is and am are accepted here.
Hi @Ash-Fred and thanks for the citation. It doesn't really apply here since Strang argues that the 3rd person pronoun, It, is what licenses the use of 3rd person verbs in all clauses. Yet, there is no 3rd person pronoun in the sentence "I, who is flying, am a man." In fact, following Strang's reasoning, not to mention basic subject-verb agreement, a 1st person pronoun in the subject position should license 1st person verbs in all clauses using that subject as a referent, resulting in the sentence, "I, who am flying, am a man." Approaching this from a theoretical syntax, descriptivist perspective, my native-speaker judgment is that "?I, who is flying, am a man" fails the test of naturalness and is, therefore, ungrammatical. I prefer ? over * to indicate ungrammaticality so as to not speak for all native speakers, though, I don't seem to be alone in this judgment. A quick search in COCA returned several occurrences of "I who am" and 0 occurrences of "I who is," where "I" is the subject of the main clause. Nevertheless, I'm sure Duolingo learners will appreciate your leniency.
Strang was probably only talking about the impersonal pronoun as we simply don't say "You are the one who are beautiful." I was rather just pointing out that, practically, subjects and verbs don't always agree with one another. Nevertheless, I have to stand corrected here; I asked seven people and five agreed with you, only one thought is was better, and the other one couldn't choose one.