Hi @Tatevik10
I think you are being reasonable to say that you just don't want to pay full price for the one night that you couldn't sleep.
Unfortunately for guests and for hosts and for Airbnb, there seems to be a number of guests who try to have an almost permanent free vacation. They check into Airbnbs and immediately make false claims (all sorts of things, from amenities to cleanliness to security issues). Then they demand a full refund and check into the next Airbnb to do the same. They do seem to get identified and banned, but it's an ongoing process. Because Airbnb deals with such issues, it's sometimes difficult for customer support to know when guests (and hosts) are being honest and reasonable, and when they are trying to beat the system. That's why I was hoping you had something to show to prove your case.
It's possible that Airbnb's position is that you were supposed to contact the host first, to give them a chance to rectify the problem. But I'm not sure whether the fact that it was 22h00 makes a difference. So sorry that I don't have more advice for you!