A friend of mine is practicing Japanese and created the sentence 私は女の人ではありません。私も男の人ではありません intending to say "I am not a woman, I am also not a man"
I offered to improve the sentence as 私は男でも女でもありません, still a little stiff but sounds more natural at least to my ears. Which got me wondering. I know that you should not use plain 男／女 to refer to others because that is rude, which this question talks about, but what about using them to refer to yourself, is that fine? Does that sound more natural than using の人?
Furthermore, if I were talking about someone else, and I said 僕の友人は男の人でも女の人でもありません does that sound reasonably natural (albeit stiff). Furthermore does 僕の友人は男でも女の人でもありません flow better, or is it just unnatural or ungrammatical?