Epidemiologist: Malaria passes into the human population when a mosquito carrying the virus bites a human who has no immunity. The malaria parasite can remain for up to forty days in the blood of an infected person. The disease cannot be passed from person to person, unless a non-infected person is exposed to the blood of an infected person. Theoretically, malaria could be eradicated in any given area, if all the mosquitoes carrying malaria in that area are exterminated. If such a course of action is carried out at a worldwide level, then the global eradication of malaria is possible.

We want to evaluate the epidemiologist's plan, so let's quick restate what that plan is:
malaria is transferred from mosquito carrying virus to human
difficult to transfer malaria from human to human
SO, exterminate all mosquitos carrying virus --> no more humans get malaria

We want to find an answer choice that indicates this plan WON'T work.

A. A person who is infected with malaria can infect a mosquito that is not carrying malaria, if that mosquito bites such a person.
This means that a mosquito that *doesn't* have the virus could get it from a human who has malaria. In our plan, there are still humans with malaria - the plan considers this a non-issue since it is difficult for an infected person to give malaria to a non-infected person. However, if this answer choice is true, an infected person could infect a non-infected mosquito (which wouldn't have been exterminated with the previously infected mosquitos), which could then infect a non-infected person. This means that there would still be a way for more people to get malaria even after exterminating all mosquitos with malaria. This is the correct answer.