@Kiym0 i would encourage you to report the incident to Airbnb and see what happens. Unfortunately, though, the guest's shady maneuver does not appear to violate a policy, so you might be stuck.
In the future, I would recommend using the Strict cancellation policy, as it closes the loophole that allows guests free cancellations like this. (The exception is in cases that meet Airbnb's criteria for Extenuating Circumstances - a loophole that does result in the host getting screwed due to the guest's failure to secure travel insurance).
Also, I strongly suggest that if anyone ever requests a date-change that would result in losing a potential booked date (as is almost certain for a same-day cancellation), you deny the request and ask that the guest cancel the booked dates.