"All life dying" is never going to happen. Life has survived on this planet through far worse cataclysmic events. And humans aren't about to go extinct anytime soon.
However, climate change has consequences. When climate shifts, fertile land becomes less fertile. When food runs out, there's famine. When there's famine there's disease and war.
Let's say it's a relatively small disruption, then only 1% of population dies off. That's not too bad? That's 70 million people. If you kill 70 people, you're a serial killer. If you kill 70 million people, you're a climate change denier.