We had two house rabbits for years. They had the run of the house whenever anyone was home and were caged the rest of the time. They were housebroken and used a litter box.
One was firmly convinced he was a cat. If you were sitting on the couch, trying to read a book, there was a rabbit ON the book. If you were trying to read the newspaper, there was a rabbit ON the newspaper. God forbid I was trying to sew....there was usually a rabbit ON the sewing machine. You get the picture....cat, yes?
The other one thought he was invisible. I'd yell, "WEASEL, GET THE F**K OFF THE TABLE!" and he'd look around like "Rabbit? A rabbit on the table? I don't see a rabbit on the table. You must be mistaken!"
You haven't lived until you have two rabbits in bed with you that don't want to share the bed. We always referred to it as the Rabbit 500.