Cleanliness is one of the most common complaints, and all too often becomes a game of host says vs guest says. As hosts (Well most of us anyway) keep our places pretty spotless because that can make are break the success of a listing, but everyone has a different standard of clean. I have had guest come through and basically white glove my place, while others have requested early check in and informed me there is no need to clean from the previous guest.
Your particular guest likely was trying to find a way to get money back or actually considered the accommodations dirty. Either way you will need to back up your case. Do you have an invoice from the professional cleaners, that has your airbnb address on it? Do you have any time stamped photos that can show that the apartment was in good status directly prior to renting?
I'm not sure if you are insinuating that they should not get back the money for the 3 nights they stayed, or if you think they should not get back anything. Either way, you could try to come to an agreement, such as offering them a partial refund of some sort. That way you avoid the hassle of going through a case with airbnb.
Sorry your first guest didn't go as smooth as you would like, and hope things work out for you.