The Future Is So Bright It Burns My Eyes.

It is not possible to destroy the whole Earth and all living beings on it with all the nuclear weapons we have. The earth has survived much worse disasters - several times. All the nuclear weapons we have can destroy many living beings - but just not all. Many primitives species of the living beings have survived much worse disasters - several times. So this species are still there.

If you destroy parts of life, then a new but similar cycle will start.