Having watched from her bedchamber, the girl said, “Gongsun Hei is handsome, to be sure, but You Chu is manly. For the man to be manly and the wife wifely: that is what is fitting." Mark Edward Lewis translates Lady Xu’s judgement of the two men slightly differently:
“Gongsun Hei was sincere and fine, but You Chu was a man. For a man to be a man and a woman a woman is what we call true order.” The trouble comes with the phrase “for a man to be manly and a wife wifely/”for a man to be a man or a woman to be a woman.” In the classical Chinese, this entire sentence is only four words long: 夫夫婦婦 (in modern Mandarin: fū fū fù fù). If you translate it literally, all Lady Wu says is: “man man, woman woman.”
How to make sense of this? The key is that in classical Chinese the number of word classes any one word can belong to is usually much larger than in modern English. The word “man” can be used not just as a noun, but also as an adjective, adverb, or verb. In this sentence the second “man” and “woman” is intended as a verb. This can be difficult to grasp for English speakers. We sometimes use the word man as verb in English (think of the phrases “man up” or “man your stations”), but those uses are quite particular to specific situations. We don’t talk about the need for men to go “manning” their way through life (and we certainly don’t talk about "womaning" your way through anything).
This gets to one of the key conceptual differences between ancient Chinese thought and the kind of thoughts we express in modern English. Another example, this time from the Analects, helps make this difference clear:
The duke Jing, of Qi, asked Confucius about government. Confucius replied, "There is government, when the prince is prince, and the minister is minister; when the father is father, and the son is son." Literally this reads: “Qi’s Jing-duke asks [about] governing to Confucius. Confucius replies: Lord lord, minister minister, father father, son son.”
You can translate this second part in several ways. You could say that the government is doing well when “fathers are fathers.” You could also translate it as “when fathers are fatherly” or “when fathers act like fathers.” But the most faithful translation would be to treat the second father as a verb: the realm does well when fathers father. This works, because the English language recognizes that being a father is not just something you are—it is also something you do. But we don’t think this way about most nouns. Fathering and mothering are things you do—but what about sonning, dauthering, or sistering? While I am sure my readers could come up with a list of responsibilities sons, daughters, or sisters have, the fact that one must do this to even talk about what it means to do sonhood or daughterhood shows how wide the gap between the world of ancient Chinese thought and our own really is.
So which came first, the role or the language which describes it? I am not sure. At first glance the former option seems the obvious answer. Because the ancient Chinese had such firm conceptions of what it meant to be a son, daughter, man, or woman, they devised words to describe people who did each. That is possible. However, I suspect (and not having studied the current state of Sapir-Whorf inspired research, it is only a suspicion) that the causality works the other way around. Classical Chinese forces you to think in terms of doing not being. I suspect ancient Chinese had such a firm conception of what it meant to be a son, daughter, man, or woman because they did not ask “what does it mean to be a man?” but “how do we do manhood?”  (Readers more up to date with the state of research on linguistic relativity are encouraged to to sound off in the comments!)
This is not a new or unique observation of my part. But it does provide an interesting translation challenge. You cannot explain all this every time you translate a verb, and just have to try your best and make the result something sensible in English. This is probably how I would translate Lady Wu’s judgement of her suitors:
“Gongsun Hei is both earnest and fine-looking, but You Chu is a man. For a man to act as a man and a woman to act as a woman—that follows [the true order of things].”
 Trans by Stephen Durrant, Wai-yee Lee, and David Schaberg, Zuo Tradition, vol III (Seattle: University of Washington Press, 2016), 1317.
 Mark Edward Lewis, Sanctioned Violence in Early China (Albany: SUNY Press, 1990), 43.
 Analects 12:11. On James Legge, trans, “The Analects: 顏淵 - Yan Yuan.” Chinese Text project. Accessed 5 July 2018.
 Classical Chinese did have copulas, so it was possible for them to say “x is y” or “Y will be z.” Indeed Lady Xu uses a copula in the first part of her assessment of You Chu: “子皙信美矣．抑子南夫也.” (“As for Zinan [You Chu], he is a man.” But they were used far less than simply smacking two terms next to each other.
 For a good example, read Ames's introduction in Sun Tzu: The Art of War (New York: Ballantine Books, 1993), 43-64