“Do unto others as you’d have them do unto you” is the positive version; “do not do unto other as you wouldn’t have them do unto you” is the negative one.
Let’s say I am treating my subordinate, Smith, in a certain way. Someone asks: “How would you like to be treated this way by Jones, your own boss?” That’s a wake-up call. “Oh wow,” I say. “I’ve been a jerk. I’ll make it up to Smith.”
There is a syllogism of the following sort:
(1) I want to be treated by Jones with respect.
(2) Therefore, I ought to treat Smith with respect.
But what is the nature of the “therefore”? Why does (2) follow from (1)?
The GR makes 3 assumptions.
First, that there is an interaction between the moral agents. I am capable of affecting Smith in a relevant way but not Shaka Zulu. I have no expectation that Shaka will treat me in any way at all; hence the GR fails to instruct me on how I ought to treat him.
Second, that I love Smith sufficiently to want to treat him justly. For I want to do good to myself; in particular, I want good to be done to me (such as by Jones), because I love myself. If I do not love (or if I hate) Smith, then (2) does not follow.
Third, that I am temporarily unaware that my actions are hurting Smith. Then the GR can jar my out of my complacency and teach me a lesson.