According to the Malbim (although there is a dispute whether it really is the Malbim) the structure of the narrative portion of the Haggadah is based on the verse in the Torah from which the obligation to tell the story is derived:
And you shall relate to your child on that day, saying “It is because of this that Hashem acted for me when I came forth out of Egypt.” (Shemos (Exodus) 13:8)
This source verse is broken up into six parts corresponding to the six sections of the story in the Haggadah.
— And you shall relate to your child
— on that day
— It is because of this
— Hashem acted for me
— when I came forth out of Egypt.
And you shall relate to your child…The first eight paragraphs correspond to this verse and teach us about this obligation to tell the story
— “We were enslaved unto Pharaoh and G-d freed us”– tells us we should relate this to our children who would also still be enslaved had G-d not taken us out.
— “It once happened that Rabbi Eliezar..” –shows that our greatest sages told the story, since the main function is to recount it for our children.
— “Rabbi Elazar, son of Azaryah, said…” –shows the duty to do so at all times.
— “Praised be the Ever-Present, praised be He…” –shows how every type of child is to be instructed at the Seder.
— “What does the wise son say…” –shows how to teach the wise son
— “What does the wicked son say…” –shows how to teach the wicked son
— “What does the naive son say….” –shows how to teach the naive son
— “And regarding the one who does not know how to ask a question…” –shows how to teach the son who can’t ask a question
–“on that Day…” –The next paragraph tells us when the obligation to tell the story applies
— “One might think that the obligation to talk…” –explains when the special duty applies.
–“saying…” — The next paragraphs contain the actual saying of the story of the Exodus
— “In the beginning our fathers were worshippers of idols…” –shows the deeper roots of the exile and the Exodus as the way to spiritual redemption.
— “Blessed is he who keeps His promise…” –shows that G-d kept His promise to Abraham that we will be enslaved and redeemed
— “It has stood firm…in every generation there are those who rise against us..” –shows that G-d continually redeems us
— “Go and ascertain what Lavan the Aramite intended to do…” –describes the beginning of the Exodus when Jacob went down to Egypt
— “And he went down…And he sojourned there…With few people…And he became there a nation…” –Great, mighty…And formidable…describes how we became a great nation in Egypt
— “And the Egyptians made evil of us…” –And the tormented us…And laid hard labor upon us…describes how the Egyptians enslaved us
— “And we cried out unto G-d… And G-d heard us…And He saw our distress… And our travail… And our oppression…” — describes how G-d heard our pleas
— “And G-d took us out of Egypt…With a strong hand…And with and outstretched arm…And with great terror…And with signs…And with wonders…” –describes how G-d redeemed us
— “Blood, and fire and smoke…An alternative explanation…These are the ten plagues…Rabbi Yosi the Galiliean says…Rabbi Eliezer says…Rabbi Akiva says…” –describes the miracles and wonders G-d did for us during the redemption
— ‘How indebted are we…How multiple, then is our debt to G-d…” –describes additional accounts of G-d’s benevolence which were not yet mentioned
–“It is because of this…” –can be read this is because of…Rabban Gamliel reads it this way…this refers to Pesach, Matzah and Maror
— “Rabban Gamliel used to say…” –explains the concrete Mitzvos ordained for the Seder: Pesach, Matzah and Maror.
— Pesach… Matzah…Maror…explains the reason for these Mitzvos
–“Hashem acted for me…” –The next paragraphs describe how we should consider it as if Hashem took us out of Egypt
— “In every generation, one is obliged to regard himself…” –emphasizes that, in celebrating the Seder, we must see ourselves as having gone out from Egypt.
–“when I came forth out of Egypt.” — The next paragraphs are the introduction and recitation of Hallel songs of praise, similar to the songs of praise that were recited when we left Egypt.
–“Therefore it is our duty to thank, praise…” — since Hashem took us out from Egypt, we praise Hashem for his kindness ending the Haggadah with a Bracha.
–“Praise G-d…” — When Israel went out of Egypt…is the beginning of Hallel which describe the going out from Egypt