Personally, I really don't care about the disappearance of coral reefs specifically. I know that may seem heartless, and indifferent, but the emotion for them just isn't there. There is no rational argument that appeals to me, either, other than scientific study/research.
The entire discussion around coral reefs has been going on since I was young and can remember(at least 20-odd years). It was always emotional (think of the children level guilt-tripping, almost), and was always "assumed" and dictated. There was never any convincing, discussing; it was just the way it is and we as young children were to accept it.
And despite all of that, we as a society have spoken the other way around and gone ahead and potentially ruined the delicate environment required for these creatures. It's who a majority of us are. Perhaps not who we should be, or who we'd like to be, but this is largely of our doing and our inability to convince those in power and the rest of society to protect the things we value.