There is a completely different meaning behind what you're claiming it says and what it actually says. If we can just inject our own meaning into words, they lose purpose.
I interpret the Golden Rule as it is written -- a bad rule, from an intolerant time where everyone was expected to be the same. It never really applied, but now we have the cognitive tools to identify it as bogus.
Why interpret it as "do what they would want, not what you would want" ? Because at its root it's asking you to have empathy and compassion. You simply can't achieve both those things without putting yourself in their shoes, and then trying to feel and understand the way they do. At that point, when you are them, you act in a way they would want, and it becomes a compassionate act.
When I was saying before that this benefits you in the end, that's true, though there is no actual reciprocity expected in this rule. It really is all about just doing good for another person.
Ask a theologian about it some time. They explain it better.