Very poor performance by AirBnb

I made a booking on Airbnbs app. I paid the quoted price given to me by the app in full. I was later contacted by the Host ***ner of the accommodation which I had booked) only to be told that there was a mistake in the advert and that airbnb had posted the ad without the hosts permission and the price was incorrect. the owner then cancelled my family vacation. I took this up with airbnb and although the personal which I communicated with were very nice and professional they refused to help me or take responsibility for this mistake. they told me it was up to the hosts discretion should he want to cancel a booking. however the booking was only cancelled due to airbnb's fault. I feel that I had paid the price quoted to me by the app and therefore the booking should stand. The apartment is still available to be booked but at a much higher price than quoted to me by airbnb. this has been my second bad experience with airbnb and I have only used them 3 times. my reference number for the airbnb booking is Hmajs82ktn