Sentence Correction (SC) | Re: During the 1890s, while at the same time a student, Willa Cather

The original sentence has some problems:
-Use of "while" + "at the same time" is redundant.
-Use of past perfect "had written is not required since there is no sequence ofevents.

Pre-thinking:
In this question while is used to denote same-time events, so correct answer choice would be:
While Willa Carther was a student in the early 1890s, she wrote theatric and music reviews....

Whit my pre-thinking I tried to find an answer, and B was the best fit. However, the structure