Official Explanation
(1) Take a First Glance (5 seconds)
Neither indicates that this question is testing Parallelism. The correct construction is neither X nor Y, and the X and Y elements must be parallel.
(2) Read for Meaning
The sentence is trying to say that it is impossible to truly understand a different culture without one of two things: having grown up in that culture or having immersed oneself in it for an extended period of time. In the original sentence, the word having comes after neither, but not after nor. Thus, when you isolate the second portion, it says that it is impossible to truly understand a different culture neither X nor immersed oneself in it for an extended period of time. The second portion does need a helping verb (nor having immersed), so eliminate answer choice (A).
(3) Find a Starting Point
Start with any difference that seems easiest to you, then move to the next easiest issue, and so on. Stop when you have one answer or you aren’t sure how to address the remaining differences. All errors for each choice are detailed in the next section.
(4) Eliminate (and Repeat)
(A) The second part of the parallel structure says that it is impossible to truly understand a different culture neither X nor immersed oneself in it for an extended period of time. The sentence needs to repeat having after or. Alternatively, the sentence could move the word having before the word neither and not repeat it: having neither grown up in that culture nor immersed oneself in it.
(B) This sentence fixes the initial broken parallelism. It is impossible to truly understand a different culture if you haven’t done one of two things: (1) grown up in that culture or (2) immersed oneself in it for an extended period of time. However, the sentence incorrectly shifts from you (second person) to oneself (third person) to refer to the same person. Either form is acceptable, as long as it’s consistent throughout the sentence.
(C) The construction not X nor Y is incorrect. The correct construction is not X or Y. If this sentence changed nor to or, it would be correct.
(D) CORRECT. This sentence fixes the initial broken parallelism. It is impossible to truly understand a different culture having not done one of two things: (1) grown up in that culture or (2) immersed oneself in it for an extended period of time.
(E) This choice has a similar error to the original sentence. The second part of this parallel structure reads as follows: It is impossible to truly understand a different culture without X or immersed oneself in it for an extended period of time. The sentence needs to repeat having after or. Alternatively, the sentence could move the word having before the word either and not repeat it: without having either grown up in that culture or immersed oneself in it.
Answer: D