This is a descriptively weakening/flaw question, and we know this because of the question stem: The reasoning is flaw because the argument...
This first sentence is a conditional: (announcement authorized by dept. head) → (important)
The next sentence denies the sufficient condition and the concludes that because of this, some announcements are not important. The flaw here is that you cannot conclude anything by denying the sufficient condition. Just because the head of the department can announce important stuff, that does not make him the only person allowed to announced important things. Once you deny the sufficient condition, the rule falls away. What this argument is doing is confusing the sufficient condition for a necessary condition: (important) → (announcement authorized by dept head). If we deny the necessary condition, then we can conclude that some announcements are not important. But the arguments stands right now, this is an invalid conclusion.
Answer Choice (A) is descriptively accurate but it’s not the flaw. Differentiating between announcements and other communications is not relevant to the argument.
Answer Choice (B) is descriptively accurate but it is not the flaw. The argument is whether these are important and that the argument too quickly denies that they’re are not important.
Answer Choice (C) is descriptively accurate, but this isn’t a flaw. The conclusion is about other announcements made by people other than the head of the department. If the head of the department doesn’t make any announcements ever, that’s fine!
Correct Answer Choice (D) is descriptively accurate and it is the flaw. This answer choices takes into account the sufficiency-necessity confusion.
Answer Choice (E) is descriptively accurate but we don’t care about opinions here.