Short answer: Because insecticides are powerful drugs specifically tailored to affect their neurological system when directly aimed, and many will leave long-lasting residual effect. Nuclear bombs not directly aimed at cockroaches may miss them underground for long enough to allow for radiation to dissipate enough for their survival.
Long answer:
There’s obviously considerable exaggeration on the widespread belief that cockroaches would survive a nuclear explosion.
Of course any exposed cockroach wouldn’t survive being hit by a missile, nor the massive forthcoming shock wave, not even the sky-high radiation levels. What is true 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 on limited nutrition and reproduce astoundingly quickly for their size.
This way, many researchers believe that cockroaches would likely survive for longer than vertebrates within any cities hit by a major nuclear accident or attack. Whether this is true or not, time will tell.
Now, insecticides are chemicals carefully selected to affect the nervous system of insects, causing death as soon as possible while lasting for a long time on surfaces (residual effect). They are designed to kill cockroaches—while nuclear attacks are designed to vanquish cities. The right weapon for the right enemy, that’s it.
nuclear-news 
And you may ask yourself, What haven’t I done? That is when even a small scale nuclear war occurs, another tohoku 9.0 earthquake hits, a meteorite stikes, there is a carrington event or any nuclear war. It is when a dozen or so, of the 400 rickety-shit old reactors from around the world, that should have never been built go off. They go off w hundreds tons of st90, cs137, co90, uranium, plutonium, yada stored next to them. Highlevel radionuclides, MOX and zirconium that will burn relentlessy into the atmosphere in a northern hemisphere already soaked with manmade and extracted radionuclides.
Such a chain of certain events, will finish off the northern hemisphere and the rest of the world a few months later.
The angry sky will be Black and red and dark with a green glow.
Insects will go first as they did at 3 mile island . People reported no flies within 5 to 10 miles of the 3 mile island meltdown, for months after it occured.
Insects like cockroaches go through a life cycle in months, where humans live sixty years. When a mutation occurs, even in cockraoch larvae, it destroys that family of cockroaches in 5 to 8 generations in accordance with wertlickis and Busbys, law of destructivle nuclear-mutation.
One serious mutation in an insect population gets them quickly. If there is fallout and radionuclide, from bombs or reactor accidents, nuclear mutations come massively and quickly, as it occured with the blue butterfly extinctions, recorded around fukushima, and in northern japan after Fukushima.
That is because insect and cockroach life cycles are short. Insects and cockroaches depend on laying lots of eggs to keep their strains going which makes it even worse.
In cockroach time, the destructive-genetic mutations, from nuclear would destroy them in few months, to a year.
That would occur, after the nests and progeny went though a few to 5 or six generations of destructive-nuclear induced, geneic mutation from dna and chromosone breaks, induced by radionuclides and radiation.
That is why, they were irradiating mosquitos and releasing the genetically-nonviable, flawed progeny into the environment in places like s america, til recently. They were creating genetically defective mosquitos, to try to kill off mosquito strains in africa and s america, that are malaria carriers.
This article stinks of propaganda and bullshit.
No doubt, A feelgood article in the face of the ultimate human insanity going on now, as crazy trump is poised to use tactical nukes on iran as dick cheney wanted in 2005 which will surely lead to larger scale war, depleted uranium usage and larger nuck detonations
Any nuclear war will probaly set off rickety reactors and fuel pools in the northern hemisphere, fukushima style. Each reactor and fuel pool containing the fallout and radionuclide equivalent of 10 thousand nuclear bombs.
Life support on earth destroyed.
When the hundreds of tons of nuclear waste dumped into the arctic, starts bubbling up from the depths. When massive nuclear armed nuclear submarines and other, have core meltdowns in the middle of the oceans from emf flashes and nuclear events, adding to the final nuclear inferno.
The human genome destroyed, all animal and insect genomes destroyed.
No one wants to talk about these things just that cockroaches can survive a nuclear war
this response will probably be censored everyone hates the dissidents and truth-tellers