What is the author's purpose in breaking the story here, at the beginning of the chapter, at its most dramatic point?From chapter 8 in The Great Gatsby
I believe you are referring to the situation in which Nick and Gatsby are talking. Nick is encouraging Gatsby to go away for awhile. Nick tells us, the reading audience:
He was clutching to some last hope and I couldn't bear to shake him free.
Then, the story breaks into a flashback about how Gatsby met Daisy originally. I believe this is actually perfectly placed because for the entire story, we knew there was history but didn't have the full scoop. Nick wants to help Gatsby realize fully and completely that he and Daisy are over. Gatsby has been so infatuated and so obsessed for so long. Now that he feels he actually has Daisy, his grip is so tight that he can't let go. This diversion helps us understand how the obsession and infatuation developed. This obsession helped create Gatsby's character. This is demonstrated in the quote:
He had intended, probably, to take what he could and go - but now he found that he had committed himself to the following of a grail.
His pursuit of Daisy had become a guest. This is important because Daisy was a person with an established life, not an object to be obtained.