How come cockroaches will live through a nuclear war?
Actually, there's debate about this. Some scientists maintain that they would survive because they'd undoubtedly beat us to the bomb-shelters. Have you seen a cockroach move? Our experts think they might simply outrun us. Then we'd open the door but wouldn't be able to get in, because the place would already be packed with cockroaches.
Other scientists think that cockroaches would be frizzled like most other things, but these scientists won't be able to prove this after the event, so we can safely taunt them with the knowledge that they would never be able to prove that cockroaches wouldn't survive.