@Bernice66
I'm amazed that a host would ask this of you. Every day I learn something new here! The slow pricing update was clearly their fault and they should obviously honour your booking at the price paid. Fortunately, if you don't agree to pay more, the host will have to cancel from their side.
I do understand that from your perspective you don't want to lose the place and would consider paying more.
If you agree to a higher price, at least make sure payment stays inside the Airbnb app.
But part of me hopes that you force this host to cancel and that it really hurts their rankings and/or superhost status ...
They should've just let it go and considered it a lesson in seasonal pricing.