Question: I don't understand this sentence:

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> In Turkmen society, the song of men and women fulfilled important but quite different functions. 
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I don't understand what "fulfilled important" means. Can anyone explain?

Answer: 
Because *but also provides* requires a verb in the preceding clause which it is countering. **but** joins two clauses both of which must be able to stand on their own. If the first lacks a verb, it is not a clause. With option D, there is no such verb. The verb there is in the *which*-clause not in the main clause. A verb in a relative clause does not act as a verb in the main clause.

Consider: 

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> Bill, *who lives in London*, but also has lived in Paris.ungrammatical
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> Bill *lives* in London but has also lived in Paris.
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Here, with *not only*:

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> Bill, *who lives not only in London*, but also has a house in Paris.ungrammatical.
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> Bill *lives* not only in London but also has a house in Paris.
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The subject here, **I**, lacks a verb:

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> I, who eat fish, but also like meat. ungrammatical
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Grammatical:

I eat fish but also like meat.

Or you can eliminate **but**:

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> I, who eat fish, also like meat.
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> * \*Vitamin C, which not only provides us with the ability to resist disease, but also helps us build our body tissues. (Ungrammatical)
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This example is ungrammatical because it is a noun phrase with no following verb. Everything after the word *which* is part of a relative clause which gives us extra information about vitamin C. We could put the relative clause in brackets:

* Vitamin c (which not only provides us with the ability to resist disease, but also helps us build our body tissues) ...

The sentence above has a long Subject, but no Predicate (no verb phrase).

For this to become a grammatical sentence we need a verb phrase after the Subject:

* Vitamin C (which not only provides us the ability to resist disease, but also helps us build our body tissues) **is very expensive**.

The example above has a Subject, *Vitamin C (which not only provides us the ability to resist disease, but also helps us build our body tissues)*, and a verb phrase *is very expensive*. For this reason it's fully grammatical.

(All of the examples from the Original question would be much more natural with the word *with*. The usual pattern is: *provide someone **with** something*)