I feel like this is a really old, easily debunked argument. Rapid change toward a much warmer climate is likely to kick off a very abrupt extinction event. Which, incidentally, has already begun.
None of this makes climate change a good thing, but it's a useful corrective to headlines that suggest we're entering some kind of uncharted territory for the planet. The planet can take a lot more than we're dishing out, even if individual species can't.