If we're workshopping this for you: "climate change" has alliteration and is only 3 syllables compared to "instability" which has a mouthful of 5 syllables.
It’s just the way the conversation happened to flow. I think everyone has an opinion on names.
For solutions I’m in favor of really aggressive carbon taxes and sanctions/secondary sanctions against that don’t implement them. But that’s the sort of thing better left to regulators and diplomats.