Hello @Nathan4021
Sorry to hear about your dog.
You can cancel your booking at any point of course and the cancellation will be processed under the cancellation policy you booked under .
When you go to cancel it will show you how much of a refund you would be entitled to.
As @Frances3408 mentions you can't expect the host to underwrite the cost of your cancellation .
I am sorry that your host isn't being clearer with you around this . If you say booked under a strict or firm policy and you are due to travel soon you may not be due a refund or may only be due a partial refund.
what the host is saying is you aren't due a refund/may only be due a partial refund under the cancellation policy you booked under - but if Airbnb want to voluntarily refund you from their own pockets they can . (They won't).
what Airbnb isn't explaining clearly is that it's not the host isn't allowing a refund -it's that you're not entitled to one under the cancellation policy you booked under . It sounds like you want the host to voluntarily refund you outside of their cancellation policy.
the best thing for you to do is see if this cancellation is covered by your travel insurance.
you can also ask your host if they get a replacement booking would they be willing to refund the host fee for any days that are rebooked .