(E) is best described as an inference from one of the premises.
Let's look at the structure of the argument:
Premise: People believed biochemical research would eventually achieve victory over microorganisms. Premise: Current research shows that they reproduce so rapidly that killing one variety will only result in more immune varieties. Conclusion: Therefore, the most rational public health strategy would be to inform people about the transmission of diseases cause by microorganisms.
(E) suggests that some prior public health approaches ignored the fact that microorganisms reproduce at rapid rate, which is a tempting inference considering the premise tells us that "current research" shows that microorganisms reproduced rapidly. Even assuming this is a valid inference, it is not the main conclusion, however. The main conclusion concerns the best public health strategy in light of the new research/ evidence regardless of the nature of prior approaches. Since (E) fails to accurately express the main conclusion, we can conclude that it is incorrect.