Really, the big problem are the instability from ripple effects. How will the world react to massive migrant crises and new, more intense conflict? To increasing economic recessions and the breaking away of old privileges? All things we are already seeing and that won’t go away anytime soon.
Now, total extinction of the species, yeah, that is very unlikely, unless something really unexpected happens. But throwing us potentially back centuries in progress, and killing a majority of people? A nuclear exchange from escalating tensions could create something like that.