@Laure54: I'm sorry your trip was cancelled due to sickness. I hope you are feeling better now.
Your host is correct. Airbnb subtracts a fee from the host's payment, therefore the host can only refund to you up to the amount they were paid. It is fortunate that you found a kind host that provided the refund that they did. Many hosts would have refused altogether as they probably would not be able re-book that soon and, therefore, would have lost money. Should you plan your trip again, please book with the same host in appreciation for his/her kindness!
If you would still like to discuss your situation with Airbnb, click the following link and scroll to find your country's information.
Thank you for using Airbnb and we hope that you will remember us for your future travels!