system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5:How are cockroaches able to survive nuclear apocalypses but die when hit with cockroach spray?
gpt
Cockroaches couldn't survive nuclear apocalypse. The explosion itself would kill roaches, just like any fire would. Radiation is less of an immediate threat to roaches than to humans, bu it would still kill them. 

Cells are most sensitive to radiation when they are dividing. Humans and other mammals have cells that are dividing all the time. In fact, chemotherapy works because cancer cells divide rapidly and the radiation from chemo kills rapidly dividing cells (that's also why you lose your hair and why men become infertile during chemo - hair cells and sperm cells divide rapidly).

Roaches and many other bugs don't have cells that divide all the time. Instead, a roach's cells only divide around the time it molts, which is about once a week when it's growing up. Molting is when a bug sheds its old exoskeleton as it's growing bigger. Since cells are usually vulnerable to radiation when dividing and a roach's cells only divide about once a week, there's only a small window during each week when radiation would kill a roach.

If there were enough radiation in the area to last a couple weeks it could still kill roaches since the young ones would have to molt at some point. Short blasts of radiation that disappear quickly would endanger humans a lot more than roaches, but fallout from nuclear weapons would stick around long enough to kill roaches too.

There's also no reason this is specific to cockroaches. A lot of insects are more resistant to radiation for this reason.