I don't think climate change, even if it lives up to the most alarmist of predictions will make humanity extinct. We'll all be gone regardless of that. A functioning civilization is composed of humans (at least in our case), and every generation of humans must have as its first priority the task of making more humans to replace the oldest (dying) generation. The fertility rate is sub-replacement, the effects of a demographic implosion cause more fertility rate issues, not less, and so that will accelerate. Too neurotic to have sex and make babies. Climate change wasn't what you needed to tackle after all.

We don't even survive for centuries.