UA ABSOLUTELY needs to fire this FA. It seems almost certain that the passenger informed the FA that there was a dog in the carrier, and persisted for a bit in her argument to keep the carrier under the seat. While I personally believe its likely the FA was an uncaring dragon who was trying to close the doors and get the wheels up over anything else in her way, I guess it's possible that she didn't LISTEN to the passenger tell her it was a dog. I'm certain she heard it, but its POSSIBLE it didn't register.
Either way, she should be fired. No-brainer. If a FA is merely moving around the cabin instructing passengers to yield to her will without at least acknowledging their complaint, she's at best a horrendous front facing employee and at worst a terrible FA who is actually risking passenger and airline safety.
The most recent statement from UA came straight from legal counsel. Let's partially defend the FA, quietly admit a major mistake, and now start manipulating behind the scenes to "make it right" with the family. I'm sure the FA union is also heavily involved here.
If there are no consequences for these types of actions, what's to stop future incidents?