The Gemara in Pesachim (36a) teaches that matzah ashirah, matzah kneaded with wine, oil, or honey may not be eaten on יום טוב ראשון, but is permitted ביום טוב שני. Rashi explains that יום טוב ראשון here does not literally mean the entire first day; rather, it refers specifically to the first night, when there is a Torah obligation to eat matzah. At that time, the matzah must fulfill the requirement of לחם עוני.
Rabbenu Channanel seems to hold that the halacha of לחם עוני applies the entirety of the night. This may be since he holds that לחם עוני is not a law merely describing the matzah but a law in the Haggadah. The Haggadah demands the presence of matzah - what matzah? לחם עוני. Hence the Haggadah obligates the eating of לחם עוני (one can also explain the Rach's opinion that all the matzah eaten at the Seder is part of the kium mitzvah of eating matzah and hence all the matzah should be לחם עוני.)
The Rambam (Chametz 5:20) however is of the opinion that entire first day of Yom Tov one can not eat מצה עשירה. This fits with the simple read of the Gemarah, בְּיוֹם טוֹב רִאשׁוֹן but why would there be a law against מצה עשירה the entire first day?
The Briskor Rav points from the terminologies of the Rambam it emerges that he doesn't hold that לחם עוני defines the matzah of the obligation of the first night, but rather it is a separate דין to have לחם עוני and that is why it is not limited to the matzah of the obligation. The דין of לחם עוני doesn't define the matzah of the mitzvah but rather is a separate halacha with its own dinim.
This approach is reflected in the Maharal Gevurot Ch. 48 that holds someone who does not have regular matzah for the seder should still eat מצה עשירה for although there will be no kium of לחם עוני it will still be a kium of eating matzah. Based upon this he does not allow for eating מצה עשירה on Erev Pesach (not like Tosfos Pesachim 35b and 99b.)
It is also clear that in the הו"א of the Gemarah that לחם עוני applies all seven days. It is clear (as the Chidushay HaRan and R' Dovid point out) that the Gemarah initially holds that the law of לחם עוני is not a law in the matzah of them mitzvah but rather is a separate law. Furthermore, the Nemukay Yosef and R' M'lonil understand that there is an actual opinion in the Gemarah that one may not eat מצה עשירה all 7 days for all 7 days one is required to eat לחם עוני.
However, this still doesn't explain why this דין of לחם עוני should apply the first day? What is unique about the first day?
Rav Yaakov Kamenetsky connects this to the Gemarah (28a, 96a) that mentions the issur chametz is Egypt was one day. למאי נ"מ? He suggests that the issur of chametz from Egypt lasts even now - and that issur is not based upon the fact that dough didn't rise but is because of a דין of לחם עוני. However, it is not clear why would the issur of the first day be linked to לחם עוני?
Rav Yaakov notes that with this Rambam we can answer the contradiction in the Haggadah if we eat matxah since it is what was eaten in Egypt as said in the beginning of the Haggadah or because there was no time for the matzah to rise as said in מצה זו? The answer is that there are two matzos. There is the matzah that we eat the first day - and that is the matzah eaten for to remember the matzah eaten as we were leaving Egypt. The matzah the rest of the days of Pesach is since there was no time for the matzah to rise.
The possuk in Reah (16:3) says תאכל עליו מצות לחם עני כי בחפזון יצאת מארץ מצרים למען תזכר את יום צאתך מארץ מצרים כל ימי חייך. The לחם עוני is connected to the day of leaving Egypt. The leaving of Egypt, as the Ramban (Bo 12:12) notes, started at night but was completed during the day. The first day in its entirety was devoted to getting out of Egypt. Based upon this we can say the source for the first day is not from the issur of chametz but rather since the entire first day is considered the time of leaving Egypt.
What is the nature of this dual leaving- in the night and the day? The dual nature is not just a historical sequence but a spiritual model. At night, darkness limits vision, one can't see properly and things are unclear. This is how the geulah began. In the nighttime phase, Bnei Yisrael followed Hashem not because they had reached a mature recognition of His truth. They followed simply because it was a way out of Egypt. It was a redemption as a way out of slavery. As explained in the maamer of Pesach 5719 (second night), this stage is marked by kabbalas ol without daas, movement without clarity, acceptance rooted in bittul rather than comprehension.
In daylight one can see properly, distinguish directions and move with intention. In the day there is clarity, resolve, and conscious commitment. The daytime leaving of Egypt represents the stage where the Jewish people follow Hashem not simply because He is pulling them out but because they themselves perceive that it is the best to follow Hashem (see maamer 5719 second night Pesach.)
We begin counting the Omer only after the first day of Pesach. The Sefer HaChinuch asks: why don’t we start counting from the very first day of Pesach? The answer is that the first day was devoted entirely to leaving Egypt. Only once we were safely out could we begin the process of internal growth and self‑refinement. This also explains why the Gemara records that R’ Yehoshua instructed his children specifically to prepare matzah ashirah only after the first day. On the first day we must eat לחם עוני because, at that stage, our role was pure submission to Hashem. It was a moment of complete bittul, without asserting our own identity. Hashem took us out, and our task was simply to follow. After that first day, however, the work changes. We are still in the “matzah mode” of humility and simplicity, but now we can begin to add some some ashirus. This represents taking our own independent strengths, personality, and capabilities and using them in the service of Hashem. It is still Pesach, still rooted in bittul, but now flavored with our own contributions.