The mitzvah of bikurim included going to the Beis HaMikdash, presenting the first fruits to the attending kohen, and reciting a prescribed formula recounting the origins of Jewish People:

וְעָנִיתָ וְאָמַרְתָּ לִפְנֵי ה אֱלֹהֶיךָ, אֲרַמִּי אֹבֵד אָבִי, וַיֵּרֶד מִצְרַיְמָה, וַיָּגָר שָׁם בִּמְתֵי מְעָט; וַיְהִי-שָׁם, לְגוֹי גָּדוֹל עָצוּם וָרָב. וַיָּרֵעוּ אֹתָנוּ הַמִּצְרִים, וַיְעַנּוּנוּ; וַיִּתְּנוּ עָלֵינוּ, עֲבֹדָה קָשָׁה. וַנִּצְעַק, אֶל-ה אֱלֹהֵי אֲבֹתֵינוּ; וַיִּשְׁמַע ה אֶת-קֹלֵנוּ, וַיַּרְא אֶת-עָנְיֵנוּ וְאֶת-עֲמָלֵנוּ וְאֶת-לַחֲצֵנוּ. וַיּוֹצִאֵנוּ ה, מִמִּצְרַיִם, בְּיָד חֲזָקָה וּבִזְרֹעַ נְטוּיָה, וּבְמֹרָא גָּדֹל–וּבְאֹתוֹת, וּבְמֹפְתִים. וַיְבִאֵנוּ, אֶל-הַמָּקוֹם הַזֶּה; וַיִּתֶּן-לָנוּ אֶת-הָאָרֶץ הַזֹּאת, אֶרֶץ זָבַת חָלָב וּדְבָשׁ. וְעַתָּה, הִנֵּה הֵבֵאתִי אֶת-רֵאשִׁית פְּרִי הָאֲדָמָה, אֲשֶׁר-נָתַתָּה לִּי, ה; וְהִנַּחְתּוֹ, לִפְנֵי ה אֱלֹהֶיךָ, וְהִשְׁתַּחֲוִיתָ, לִפְנֵי ה אֱלֹהֶיךָ. וְשָׂמַחְתָּ בְכָל-הַטּוֹב, אֲשֶׁר נָתַן-לְךָ – You will answer and say before your God, “The Aramean pursued my father, and he descended to Egypt, and dwelled there, where he became a nation, great and many. Egypt cruelly afflicted us, and they gave us hard labor. We cried out to Hashem, God of our fathers, and He heard our cries, and saw our suffering and affliction. He extracted us from Egypt with a strong hand and an outstretched arm, with great wonders and miracles; and brought us to this place. He gave us this land, flowing with milk and honey. And now, see I have brought my first fruit, which God has granted me, and I place it before God,”.
He shall place it before God and bow, and rejoice at all the good he has been given. (26:5-11)

On Pesach, the Hagada quotes from this portion, which is odd, because the actual primary record is in the book of Shemos. This section is a secondary paraphrase; and is not about leaving Egypt at all!

When we remember leaving Egypt, why does the Hagada quote from bikkurim and not from its proper historical place?

The Sefer HaChinuch explains that the mitzvah of reciting the story of Exodus is not limited to the history; we must also contextualize it through a lens of gratitude, which the historical sections do not have.

The bikurim section has a context that the historical sections do not. The whole theme of bikurim is about gratitude for the Land of Israel, because having once been oppressed slaves in Egypt, we have a finer appreciation for liberty and freedom.

We can comprehensively learn the rules of gratitude from the thanksgiving offering – the Korban Toda – which was brought if someone was released from jail; crossed an ocean or a desert; or recovered from illness.

The offeror presented an animal offering, of which only a small portion was burnt or taken by the kohen, and with it, 40 accompanying loaves of bread. These were essential parts of the offering and had to be consumed within the day, and were otherwise subject to the law of leftovers and would have to be destroyed.

The Torah’s treatment of gratitude consistently includes an intrinsic requirement to publicise it. One man is not supposed to eat an entire animal and 40 loaves of bread on his own.

He is supposed to invite all his friends and family.

The Korban Pesach and bikurim share this quality – an entire roast animal that is to be consumed after a full meal, in a tiny amount of time, before midnight. You need to have a lot of people at the Seder and tell the story of Egypt.

In a certain sense, the Korban Pesach a national Korban Toda. The Jewish People were liberated from slavery; crossed an ocean and a desert; and when they stood at Sinai, were healed of all illness.

Accordingly, it makes a lot of sense that bikurim and the Hagada do not quote from Shemos, and instead tell a story about gratitude and appreciation.

The concluding statement in Bikkurim says it all – וְשָׂמַחְתָּ בְכָל הַטּוֹב אֲשֶׁר נָתַן לְךָ ה אֱלֹהֶיךָ וּלְבֵיתֶךָ – you should rejoice in all Hashem does for you, for each thing individually – בְכָל הַטּוֹב.

A Jewish expression of gratitude is public and spelled out.