@Donna249
Donna, I notice on your Peggy's Cottage listing you do state you have a TV, but you give no details.
This problem used to come up frequently and Airbnb have included an edit box to show exactly what sort of TV is offered to guests. It stops these problems.
If you go to your listing details page and under the amenities section click the TV icon and this box will appear.......
It is imperative that you fill that edit box out, if you don't the guest may well have reason to complain because, the omission was your fault not Airbnb's, or the guests. Before Airbnb offered this box the host could legitimately say......"Well Airbnb don't give me an option to show what I offer"....but that's not the case any more. Here is what the guest sees in a general amenities search if you have edited TV......
When you fill that edit box out the features you offer will show alongside the TV icon, and if they don't appear there you can refuse the guests request.....they simply did not read the description carefully.
You do have to be precise in what you offer because guests associate amenities with what they are used to. This guest might only use cable at home and it wouldn't cross their minds that you don't offer it.....to them, it's just TV. You have to be specific! My feeling is you are going to have to offer some sort of compensation Donna, sorry to say that but, the guest does have a case!
Cheers........Rob