Cancer isn't something that humans develop and control. It's also very unlikely to kill 20-year-olds. On the other hand, it's almost guaranteed if you happen to live long enough. Finally, getting cancer doesn't mean that everybody around you also gets one. Getting hit by a nuke is something that is totally under human control, it's not going to discriminate by age or gender, and is likely to wipe out most of the humans you care about along with you.

A better comparison would be climate change vs nukes. If you have the time to worry about the former, you should also worry about the latter since if the nukes go off, we won't even get a chance to get killed by the environment.