@Helene401
The host can NEVER cancel. Don't ever do it! Even if the guest asks you to or sends you a cancellation 'request' via Airbnb. What is likely happening here is that the guest is seeing that if they cancel they are still going to be responsible for a portion of the booking based on your cancelation policy and/or they will still have to pay for the Airbnb service fees.
The guest can cancel themselves as it was their error or you can call Airbnb and ask them to work it out with the guest. You will be heavily penalized if you cancel so don't do it.