In "The Author to Her Book" by Anne Bradstreet, the extended metaphor (referring to the narrator's writing as her "offspring") conveys her difficult relationship with her work.
The first line of the poem refers to the work of writing as "ill-formed", conveying that the narrator is not satisfied with its outcome-- or at least not satisfied enough to share it with the world. She wants the work, like a child, to remain by her side. However, when the writing is "snatched from thence by friends" and "exposed to public view", the narrator is embarrassed by the fact that "all may judge" it. The narrator feels as if she has failed, like a mother who has inadequately raised her child. The line "I washed thy face, but more defects I saw" refers to how the narrator tirelessly tries to revise the work after it has been exposed but is unsuccessful; a mother washes the face of her child to clear it of dirt and make the child presentable, and the narrator's revisions are parallel, trying to make it more fit for the (unintended) audience.
The narrator's attitude is complex because, although she is convinced from the beginning that her writing is subpar, it is nonetheless special to her, thus she is irritated when it is taken without her permission. Towards the end, she feels as if the writing is no longer hers but everyone's. As a result, she speaks to the work, saying "if for thy father asked, say thou had'st none." She wants to believe that the work is hers in the same way that it once was-- before it was released. Her words reflect how truly alone she feels, labeling herself as a single "mother". Her writing and her insecurities surrounding it portray her complexity as a character -- she writes, but she doesn't want her writing shared. Once it is released, however, she attempts to revise, as if a new standard has been created for her own work. The narrator seems to now be fighting writing, rather than appreciating it as her "offspring" like she did before it was publicized.