@Jeff75 - When your guest made the reservation, they paid Airbnb in full. Airbnb holds onto that money until the reservation (in October) is/was to happen. If you agree to refund the guest monies outside of your normal cancellation policy - which in this case is set to Strict - they will collect that additional money from you NOW. The same holds true for the money they refund the guest - which would be 50% - they will give that back to the guest now. So, yes, you are correct, you pay whatever additional funds you are going to refund, right now, and Airbnb will pay you for the portion you were to receive, in October. It sucks. It also encourages hosts to not refund beyond their refund policy.
From an accounting perspective, the reduction of the principle they were going to keep until October for investing is arbitrarily being paid back by you, so you must make the monetary sacrifice for that decision. Their dedicated funds, stay dedicated until the date of payout. I won't say I agree with this, but it is the way they handle it and it's in the terms of service. Basically, you give away that money for a period of time.
The same sucky financing happens with Extenuating Circumstances refund. The guest doesn't arrive for some unforseen circumstance and doesn't cancel their reservation online. You are stuck holding the bag for a period of days where you can't rent becasue there is an active reservation and you get paid. Then Airbnb grants the refund and they deduct the funds from your future payout. So, not only couldn't you book to recoup the costs that you know are coming, but you will see a future reduction hurting later. You get the money for a short period of time and then have to give it back.