"Do unto others as you would want done unto you" only works so long as we can already discern between being kind or unkind to ourselves. The kindness we extend to ourselves is not only measured by the quality of thoughts we have about ourselves, but also by the quality (and quantity) of the thoughts we entertain about others.
When we abandon unkind thoughts of others, we first and foremost extend kindness to ourselves.
The quagmire of entertaining less than kind thoughts sinks the mind into the quicksands of suffering..."entertaining" is the pivotal word.
Most of the day we're not thinking intentionally, meaning that we're not directing the mind to think in a particular manner or solve a particular problem. Invited or not, thoughts just keep coming into the mind. Where we have a say is in whether or not we entertain them.
Thoughts are very much like a movie, in that if they are of the slightest bit of interest to us, we'll become so engaged that are moods will move with them. While we might not yet be able to prevent certain thoughts from entering into the mind, it's through the practice of meditation, practicing mindfulness, that we are able to choose whether we engage with them or not. When we engage, we proliferate, and when we proliferate, the accompanying mood stays.
So being kind to ourselves first and foremost begins with not entertaining the thoughts that create suffering in the mind. When we're being kind to ourselves as such, we're interacting kindly with the world around us, thus not bringing suffering to ourselves or others.
It's a happiness that doesn't hurt.