As a writer myself, I can verify that some stories seem to write themselves. This means that when you start writing them, you (as a writer) know instinctively what is going to happen. It seems as if the story is unfolding on the page for you, as you write.

Writers have different styles. Some writers plot out stories; some plan them in detail; some writers make complete outlines and adhere to them. Most of the time, a writer works through a certain point and then has to struggle over one choice or another. But this is not what the phrase is referring to.

The phrase is referring to writers who “write by the seat of their pants.” That is, people who sit down and start writing with nothing but their instincts to guide them. (It’s not that “pantsers” never have trouble writing. It’s just that sometimes when they’re writing, they get so tuned into the story that it flows from beginning to end.)

Magically, the story just seems to come out on the page, with all of the choices made, as if the characters are whispering in the author’s ear.

That’s what it means when the story writes itself.

As far as the “she” in your example, I would need more examples of her tone to know what she is implying. She could be making fun of his ability; or she could be being humorous over how hard he is working to bleed every word on to the page; or she could be referring to how easy it is to read what he wrote.

The phrase is usually used sarcastically to denote that an idea is, in fact, horrible, or possibly that the author is lazy or not trying.

the most common reason to why a book would ‘write itself’ would be because the idea was so strong.