The mishna provides the format for sippur yetzias Mitzrayim, maschil b'genus u'mesayem b'shvach. We begin by shamefully recounting our degradation: we were idolatrous and slaves. We conclude by thankfully celebrating our privileged status: Hakadosh Baruch Hu miraculously redeemed us and sanctified us as His chosen people.
What is the source for this format and what is its underlying significance? Rambam does not explicitly address this question. His words, however, implicitly provide a beautiful answer.
Both these festivals, I mean Sukkos and Pesach, inculcate both an opinion and a moral quality ... As for the moral quality, it consists in man's always remembering the days of stress in the days of prosperity, so that his gratitude to God should become great and so that he should achieve humility and submission. Accordingly, matzoh and marror must be eaten on Pesach in commemoration of what happened to us. Similarly, one must leave the houses and live in sukkos, as is done by the wretched inhabitants of deserts and wastelands, in order that the fact be commemorated that such was our state in ancient times: "ki baSukkos hoShavti es Bnei Yisroel - that I made the children of Israel dwell in sukkos", and so on [Guide 3:43]
Rambam had already developed this idea earlier in the Guide as well.
As for the reading on the occasion of the offering of the bikurim - first fruits, it also is conducive to the moral quality of humility, for it is carried out by him who carries the basket on his shoulders. It contains an acknowledgement of God's beneficence and bountifulness, so that man should know that it is a part of the divine worship that man should remember states of distress at a time when he prospers. This purpose is frequently affirmed in the Torah: "v'zocharta ki eved hayisa - and you shall remember that you were a servant", and so on. For there was a fear of the moral qualities that are generally acquired by all those who are brought up in prosperity - I mean conceit, vanity, and neglect of the correct opinions: "pen tochal v'savata u'batim tovim tivne - lest when you have eaten and are satisfied, and build good houses" and so on. It is because of this apprehension that the commandment has been given to carry out a reading every year before Him, may He be exalted, and in presence of His Indwelling, on the occasion of the offering of bikurim - first fruits. You also know already that the Torah insists upon the plagues, which befell the Egyptians, being always remembered: "l'ma'an tizkor es yom tzeitscha - that you may remember the day that you came out", and so on. And it says: "u'l'ma'an t'saper b'oznei bincha - and that you may tell into the ears of your son", and so on. [ibid 39]
The Torah protects us from becoming haughty and feeling entitled. When enjoying prosperity, we are to remember days of penury. When experiencing success, we are to recall suffering. For this reason the pilgrim upon bringing bikurim does not simply say "thank you, Hakadosh Baruch Hu." Instead he is maschil b'genus u'mesayem b'shvach by reliving our degradation and only then thanking Hakadosh Baruch Hu for the prosperous harvest.
We also eat matzah (= lechem oni) and maror and remember yetzias Mitzrayim for this reason as well. Accordingly, Chazal instructed that we recount sippur yetzias Mitzrayim in the humbling format of maschil b'genus. Moreover, the central text for the sippur is arami oved avi, the parsha of mikreh bikurim, which serves as the source for maschil b'genus.