The answer to your question would be that this sentence is wrong because the pronoun and antecedent do not agree with in number. That is, the correct option would be A.
The NP "a writer" is singular and the pronoun referring back to this subject is plural "they". However ungrammatical as it may be, this use of the pronoun "they" is known as "singular they". Singular they is the use in English of the pronoun "they" and any of its derivative forms (them, their, theirs, and themselves) as a gender-neutral singular pronoun.
