Why was Pulp Fiction constructed in a non-linear manner?
What is the main reason for it?
I don't think Tarantino has ever explained, so all you'll find are attempts at an explanation, like this one:
But after reading the script several times, I have come to the conclusion that Tarantino, whether he intended it or not, hit upon nonlinearity as the only way he could tell one particular storyline in the script, the tale which comprises the ‘moral’ center of the movie, the story around which the screenplay’s Themeline revolves. That story involves the fates of Jules and Vincent.
Tarantino goes to great lengths up front, enormous gobs of seemingly inane dialogue (p. 7-17), to establish Jules and Vincent as sort of philosopher-goofballs, whose vocation, as it happens, is to whack people. So Tarantino has set us up to anticipate yet another post-modern ironic take on violence, the breakdown of society, blah blah blah.
But what is really going on, in my opinion, is far more traditional: A tale about morality and humanity, one guy who finds it (Jules), and one guy who does not (Vincent). The guy who finds it, lives. The guy who does not, dies.
What works so beautifully with the nonlinear approach to Pulp Fiction is that:
We get a chance to witness the opening shoot-out and wonder how it has anything to do with anything else for 141 pages – until we finally see it pay off.
We get a chance to meet Jules and see the ingrained violence of his world, setting the bar especially high for him to change.
We get a chance to live with the Fourth Man’s stunned expression after he unloads his .357 to no effect and his pursuant comment, “I don’t understand,” knowing that something odd took place at the end of that scene; again how will this pay off?
We get a chance to live with Vincent who doesn’t show a depth of soul akin to Jules (and ends up dying for his lack of human potentiality).
We get a chance to see another tortured soul with a choice, Butch, who makes the right decision (dignity in refusing to throw the fight), then makes another and even harder choice (goes back to help save Marsellus, the guy who wants him dead), but whose ‘moral’ decisions result in earning him his ‘freedom’ and the ability to live a new life.
All that story material, so when we rejoin the Jules’ storyline, we ‘get’ Tarantino’s moral landscape. When Jules has his life-altering confrontation with Pumpkin, and a single twitch of a finger could turn their little world into an instant bloodbath, we buy the meaning of the last words Jules says to the nervous robber, “The truth is you’re the weak. And I’m the tyranny of evil men. But I’m tryin’. I’m tryin’ real hard to be a shepherd.”
In sum, Pulp Fiction is a great example of nonlinear storytelling because it serves the story.
From Quora (bolded is mine):
The chronology of the film is structured to prevent audiences from realizing that the end of the film is really the middle and near the middle is really the end.
By Jon Mixon
[The nonlinear plot] serviced the experience of the film and further engaged the audience...The audience was engaged by jumping back and forth, always wondering where the A story would intersect with the B story and C story and D story. It created an invested audience that wanted to revisit the film to see the many connections in the background of each scene and sequence as they figured out how everything was connected. It's not an easy structure to pull off, but if done right, a writer and/or director can keep an audience invested even moreso than they would with a linear structure. You keep them guessing. You keep them invested. You keep them engaged. That's the key to a successful film and script.
By Ken Miyamoto
Tarantino is famous for his tributes to other movies and genres: it is most likely, a tribute to himself and his previous movie Resevoir dogs, in which the story is not told in chronologial order, but jumps back and forth in time (in that case it was an hommage to old noir movies, such as Kubrick's The killing).
He does the same in Kill Bill.