A favorite passage of mine from Mengzi (Mencius) is this one:
That which people are capable of without learning is their genuine capability. That which they know without pondering is their genuine knowledge. Among babes in arms there are none that do not know to love their parents. When they grow older, there are non that do not know to revere their elder brothers. Treating one's parents as parents is benevolence. Revering one's elders is righteousness. There is nothing else to do but extend these to the world (7A15, Van Norden trans.)
One thing I like about this passage is that it assumes love and reverence for one's family as a given, rather than as a special achievement, portraying moral development as a matter of extending that natural love and reverence to new targets.
Similarly, in passage 1A7, Mengzi notes the kindness that the vicious ruler King Xuan exhibits in saving a frightened ox from slaughter, and he urges King Xuan to extend similar kindness to the people of his kingdom. Mengzi says that such extension is a matter of "weighing" things correctly -- a matter of treating similar things similarly and not overvaluing what merely happens to be nearby.
Contrast this approach with "The Golden Rule": "Do unto others as you would have others do unto you". Contrast it also with the common advice to imagine yourself in someone else's shoes. Golden Rule / others' shoes advice assumes self-interest as the starting point. While Mengzian extension starts by assuming that people are already concerned about nearby others, and takes the developmental or cognitive challenge to be extending your concern beyond a narrow circle, The Golden Rule / others' shoes thinking starts by assuming egoistic self-interest, and takes the developmental or cognitive challenge to be generalizing beyond one's own self-interest.
Maybe we can model Golden Rule / others' shoes thinking as follows:
(1.) If I were in the situation of Person X, I would want to be treated according to Principle P.
(2.) Golden Rule: Do unto others as you would have others do unto you.
(3.) I will treat the person according to Principle P.
In contrast, maybe we can model Mengzian extension as follows:
(1.) I care about Person X and want to treat them well.
(2.) Person Y, though perhaps more distant, is relevantly similar.
(3.) Therefore, I should also treat Person Y well.
There will be other more careful and detailed formulations, but this simple sketch captures, I hope, how radically different these two ways of modeling moral cognition are. Mengzian extension models general moral concern on the natural concern we already have for those nearby, while Golden Rule / others' shoes thinking models general moral concern on concern for oneself.
I like Mengzian extension better, for three reasons.
First, Mengzian extension is more psychologically plausible. People do, naturally, have concern for and compassion for others around them. Explicit exhortations aren't necessary to bring this about. This natural concern for and compassion for others is likely the main seed from which mature moral cognition grows. Our moral reactions to vivid, nearby cases become the bases for more general principles and policies.
Second, Mengzian extension is less ambitious -- in a good way. The Golden Rule imagines a leap from self-interest to generalized good treatment of others. The Golden Rule is sometimes excellent and helpful advice, perhaps especially for people who are already concerned about others and thinking about how to implement that concern. But Mengzian extension has the advantage of starting the cognitive project much nearer the target, involving less of a leap, since it only moves from natural concern about nearby cases to similar treatment of relevantly similar but more distant cases.
Third, Mengzian extension could arguably be turned back upon yourself, if you are one of those people who has trouble standing up for your own interests and rights. You would want to stand up for your loved ones and help them flourish. Applying Mengzian extension, extend the same kindness to yourself that you would give to give to others you care about. If you'd want your sister to be able to take a vacation, realize that you owe the same courtesy to yourself.
Although both Mengzi and Rousseau endorse the motto that "human nature is good", and have views that are similar in important ways (as I explore here), this is one difference between them. In both Emile and Discourse on Inequality, Rousseau emphasizes self-concern as the starting point, treating natural pity or compassion for others as secondary and derivative. He endorses the foundational importance of the Golden Rule, concluding that "Love of men derived from love of self is the principle of human justice" (Emile, trans. Bloom, p. 235).
This difference between Mengzi and Rousseau does not, I think, reflect a general cultural difference between ancient China and the West. Kongzi (Confucius), for example, endorses something like the Golden Rule: "Do not impose on others what you yourself do not desire" (15.24, Slingerland trans.) Mozi and Xunzi, also writing in period, imagine people acting mostly or entirely selfishly, until society artificially imposes regulations upon us, and so they cannot see Mengzian extension as the core of moral development. (However, also see Mozi's argument for impartial concern that starts by assuming that one is concerned for one's parents [ch. 16].) The extension approach is specifically Mengzian rather than generally Chinese.