In The Handmaid's Tale, Offred makes a point of saying that she is not writing this down. Why is that important?

The narrator of this novel is what is known as
"unreliable" although not for the usual reasons one uses this term. Normally an
unreliable narrator cannot be trusted to give the whole story because they may be
dishonest, or ignorant of the truth, or intentionally trying to deceive their audience.
They may also be sociopathic or insane. In Offred's case, it is possible, given the
extreme controlling nature of the society she lives in, that her every communication and
movement is watched by the government. And so maybe her entire story is being coerced.
Also, we learn at the book's end in a strange epilogue that her story was a "found"
record of some kind, and its provenance is portrayed as dubious, even as the
circumstances she portrays have apparently become even more pronounced in the future
society discussing her manuscript.