Talking trash, disrespecting, saying something negative about someone or something. Subtext is that the thrower often ends up looking worse than the throwee.
It's a new one to me, too.
I've heard two similar:
"holding anger is like grasping a hot coal with the intent of
throwing it at someone else; you are the only one who gets burned"
-supposedly Buddha
"resentment is like taking poison and waiting for the other person
to die"
-Malachy McCourt
In this instance, I'm not sure the subtext applies; I think most people probably agree with the First Lady...