The prediction, as the fantastic opening paragraph explains, was made by "many scientists" (a perennially referenced but rarely identified authority), and is "based on sound, biological facts." Ipso facto, we're doomed. Dooooooooomed!
The opening graf, should your eyes fail you:
Many scientists agree on the grim possibility that the earth may some day face annihilation by hordes of giant insects. Their prediction is based on sound, biological facts. The startling theory that common insects are capable of evolutionary growth of one hundred or even one thousand times their present size has long been considered likely by the keenest scientific minds.