If the "departure cleaning fee" is mentioned in the listing at the time of your booking, then you are obligated to pay or the host will have reason to cancel. If the fee is not disclosed at the time of your booking, then you can refuse the fee request and the if the host cancels, then Air BNB will levy host cancellation penalties.
More importantly, @Michael774, is preserving your travel plans and you might want to communicate with the host about the additional fee. You might be able to come up with a compromise that works for both of you. Or, you can cancel now and find another suitable place. Good luck and keep us posted!