@Matthew1694
I assume you did the cancellation from your end? That message thread is vague and won't help you because it doesn't specify how much you would be refunded. Even if it did, it is at the host's discretion. Of course, I don't think it's okay to go back on what he promised, but he is within his rights to do so and stick to the cancellation policy you agreed to when you booked.
I think your case really rests on what was advertised versus what you got. So, was climate control advertised? Was it not working, or simply not there at all? Were there other amenities listed that were not provided? What about the pool and spa? I see that the pool is mentioned in the actual listing title (so I trust it's listed in the amenities too). Why was there no access to it, exactly? Was this bait and switch, or was there a particular problem at the time of your stay? You say you didn't think the problems would be resolved, but the host says differently in the message thread. It's hard to know what's going on as you haven't explained why you couldn't use the pool.
The Aircover policy states that guests will be refunded if a major amenity is missing. So, it depends on what is considered major or minor. I suspect that the reason Airbnb refunded you 10% because they considered the issues to be minor, or that you didn't give the host a chance to resolve the problems.
I would say that the climate control could be quite major, depending on the temperatures in the place you stayed, i.e. if it was very hot or very cold. I would personally argue that the pool was a major amenity that was advertised and not provided. It could very well be the reason why a lot of guests book this listing. Why else would it be mentioned in the listing title?
Anyway, IF the issues were not resolvable, e.g. there was actual no climate control in the listing, rather than it being broken, which the host might have been able to fix, and you were not going to be able to access the pool and spa for the duration of your stay, rather than just the first night, then I would go back to Airbnb and argue the case that major, advertised amenities were missing and the host would not solve these problems (if you have evidence of that) and that is why you needed to leave.