It undermines leadership efforts. One of the many challenges an organizational leader faces is buy-in from his people. What he doesn't need is one of his appointed deputies barking insults behind his back, because doing so only erodes the trust that was built.
It establishes your reputation as a gossip hound. Authenticity is about dealing with conflict as it happens rather than waiting for the leader to leave the room. When people know where you stand, they also know what you stand for