@Delanie1 How absurd. Why on earth would someone with cat allergies book a place he was clearly informed had cats? And Airbnb's response is outrageous. If you have kids and your guest doesn't like kids, are we supposed to farm them out or lock them in their rooms? Maybe you should ask them that.
I'd ask the guest to cancel the rest of his booking, and tell him that you will refund whatever days you are able to rebook. If he won't cancel it, get Airbnb to. Make sure Airbnb has screen shots of your message to him pre-booking re-iterating that you have cats. This is 100% on the guest. Stand your ground.