Climate change does indeed happen naturally. That doesn’t mean it can’t also be caused by human activities. The real lesson from past, natural, rapid climate change is that it produced significant extinctions. In other words, life got difficult.
The good news is that the fossil record shows that Earth always bounced back to full biodiversity. But this typically took 5-10 million years. Our planet will almost certainly be fine again, but only after countless generations have had to survive on a severely damaged and far less beautiful world.