Sentence Correction

Answer is D.
First concision: remove A,B and E.
From C and D: parallelism: 'having' is a gerund and this has to be compared to association - a noun.
That is why choose C - her smile, her association

Here's something to think about:

Does "an explanation for" have exactly the same connotation as "explain"? I don't think so.

Here's another example:

a) The professor explained the solution to the math problem.
b) The professor gave an explanation for the solution to the math problem.

Obviously, a) is preferable here.

But in the following case:

a) The art historian explained the Mona Lisa's smile.
b) The art historian gave an explanation for the Mona Lisa's smile.

I think it depends on what you're trying to say. In a), the connotation to me is that the art historian explained the physical attributes of the smile and anything else about it "on the surface," such as the fact that it resembles an archaic smile. However, I think b) implies that the art historian went into the deeper, underlying causes of the smile and any meanings behind it, such as the Mona Lisa's emotional state, the character and disposition of the artist himself, specific things that the smile might symbolize, etc.

It's kind of hard to test these shades of meaning in a multiple-choice format. Conciseness is good, but--depending on what you're trying to say--not always better.