How are the terms for "male/female" and "man/woman" divided exactly?
It's hard for average Chinese to answer the etymology of the words, I think. Why isn't &quot;son&quot; 男儿? For me, I would say because &quot;男儿&quot; has another meaning in both classic and modern Chinese.

男儿 young man,  vital man.
男儿何不带吴钩，收取关山五十州. By the poet 李贺 in 唐 Dynasty
nán ér hé bù dài wú gōu ,shōu qŭ guān shān wŭ shí zhōu.
As a man, why not I take the sharp swords to retrieve the lost lands?

In classic Chinese,

子 infant, child
儿 teenager, son
女 daughter, female(gender)

In modern chinese(actually, in vernacular Chinese from 宋 dynasty), 子 and 儿 are common suffix words. I believe this is how 女儿 and 儿子 evovle.