I would suggest you read Airbnb's terms of service. I think you'll find the host and Airbnb are not responsible for the actions of others or insuring guests for others' actions. If you had a friend stay at your home and someone broke in and stole their ring, or another of your guests stole it, you would not be responsible. I don't know if your homeowner's policy would cover it, since such things generally cover the property of the homeowner, not temporary guests. Maybe the host has such a policy and you could get reimbursed after the deductible. But normally, one is repsonsible for insuring their own belongings. If you were injured on the property because of the owner's neglect, then they and their insurance policy could be held liable.
I care that you lost your ring and that it hurts. Sometimes people do crappy things in life and leave those they harmed with the resposibility for dealing with it, along with the pain. Whoever stole your ring was a thief, but you don't have to take on an identity of being their victim, that gives them way more power than they merit. They stole your ring, not you, and not the one who gave it to you.
