Any announcement authorized by the head of the department is important

Any announcement authorized by the head of the department is important. However, announcements are sometimes issued, without authorization, by people other than the head of the department, so some announcements will inevitably turn out not to be important.

The reasoning is flawed because the argument

(A) does not specify exactly which communications are to be classified as announcements - WRONG. Irrelevant.

(B) overlooks the possibility that people other than the head of the department have the authority to authorize announcements - WRONG. 2nd best candidate but even if others have authorization authority it does not help in knowing why some announcements would not be important. Here itself it loses.

(C) leaves open the possibility that the head of the department never, in fact, authorizes any announcements - WRONG. Altogether wrong for reasons that it nullifies the passage itself.

(D) assumes without warrant that just because satisfying a given condition is enough to ensure an announcement's importance, satisfying that condition is necessary for its importance - CORRECT.

(E) fails to distinguish between the importance of the position someone holds and the importance of what that person may actually be announcing on a particular occasion - WRONG. Goes offtrack.

Answer D.