Can you please offer analysis of the core, and how to approach correct answer in this question?

I came up with the following:

If PMS (popularity of a music scale) were a result of SC (social conditioning) -> Diverse mixture of diatonic & non-diatonic scales

If diatonic dominates -> PMS is not result of SC

Conclusion: Popularity of diatonic -> innate dispositions

Inference: PMS not result of SC -> innate dispositions

But I got lost after this... Any help would be appreciated!

The argument's evidence is enough to establish that the popularity of a musical scale is not determined by social conditioning. We can establish this from the conditional relationship in the second sentence and the denial of the necessary condition in the third sentence.

SC --> DMS
~DMS

therefore we know that

~SC

(Notation Key: SC = social conditioning, DMS = diverse mixture of scales)

This does not prove however, that the popularity of diatonic music can be attributed only to to innate dispositions of the human mind. The conclusion is simply too strong and fails to consider other possibilities.

The most important word in the whole argument is "only" in the conclusion. Way too limiting. The popularity of diatonic music may not be attributed to social conditioning, but it could be a result of a combination of social conditioning and innate dispositions of the human mind. Best expressed in answer choice (D).

(A) is not true. The argument does not fail to address this possibility for while the popularity of diatonic music is discussed, the argument never claims that people do not appreciate nondiatonic music more.
(B) is irrelevant. The argument does not need to explain how innate dispositions increase appreciation, nor does the argument claim that innate dispositions actually do this at all.
(C) is irrelevant. The argument does not need to explain the existence of either form of scale.
(E) is way out of scope, as nonhuman animals have no bearing on this argument.

Does that clear this one up? By the way, following the chain of logic in this question is much more difficult than simply eliminating the clearly incorrect answers, but I'm glad that you're taking the time to really understand the question.