I would not give a refund. I had a nice lady cancel 2 days before her arrival and I did not refund. Of course she didn't stay so there was no review. If I had re-rented it, I would have refunded.
If he cancels, he needs to do it online. Then airbnb gives you the option to refund or not.
For me, I would not have booked him because it would be too stressful trying to get cat dander out. You never know the level of someone's allergic response. It can put someone in the hospital. That being said, I divided my house completely so we don't share space. My idea is to make money--and that has worked out very well--and enjoy myself. If someone is too high maintenance, I won't do it. But I'm old 🙂 and I've learned that the hard way. If you say you have a cat, I don't know why he even tried to book with you. He sounds like he's only thinking of himself (and the tv). You can talk to airbnb and see if they'll remove the reviews. My one mutual cancellation I did charge for the night she stayed but airbnb blocked the review process on both sides because they felt I was reasonable. I lost the money for the rest of her stay but that's because neither she nor I wanted her to stay. It was a bad fit. I probably re-rented it anyway.
If the guest breaks any rules or does not agree to your posted statements, airbnb will support you (in my experience). In other words, if he says he's cancelling because he doesn't have the whole place to himself, then he is breaching the contract. He is not giving notice and that is breaching contract. All money goes through airbnb which is the reason for doing this! You don't have to discuss the refund with him. Tell him to call airbnb. Some people do not read the description given--that is their problem, not yours. I work hard to be extremely clear about shared and private space. Also when someone asks for too much--like you taking your cat elsewhere, that indicates he is a high maintenance person who does not consider others. If a negative review comes out of this, you can repsond publicly and also rate him. Bottom line, you went to extraordinary lengths to provide for him, and then he bails. Unacceptable. Keep the money. If you are able to re-rent you could refund through airbnb--but I wouldn't even tell him that or he will be bothering you about it.