Why do cockroaches survive nuclear attacks but are killed by a raid?
The short answer: because insecticides are powerful drugs specifically designed to affect your neurological system when directed directly, and many will leave long-lasting residual effects. Nuclear bombs not directed at cockroaches can lose them underground long enough to allow the radiation to dissipate long enough for their survival.
The long answer:
There is obviously considerable exaggeration in the widespread belief that cockroaches would survive a nuclear explosion.
Of course, any exposed cockroach would not survive the impact of a missile, or the massive shock wave coming, or even the high levels of radiation. What is certain is that insects are generally more resistant to radiation than vertebrates because of their smaller size and filtering exoskeleton, and that some pest cockroaches are well known for being able to survive with limited nutrition and reproduce amazingly quickly for their size.
In this way, many researchers believe that cockroaches would likely survive longer than vertebrates within any city hit by a major nuclear accident or attack. Whether this is true or not, time will tell.
Now, insecticides are carefully selected chemicals to affect the nervous system of insects, causing death as soon as possible while lasting a long time on surfaces (residual effect). They’re designed to kill cockroaches. While nuclear strikes are designed to defeat cities. The right weapon for the right enemy, that’s all.