In the article by Rabban Gamliel (in Mishnah Pesachim 16:1 and in the Passover Haggadah), there is a dispute among the sages regarding the interpretation of the statement, "Anyone who has not said these three things on Passover has not fulfilled his obligation." The first opinion is whether not fulfilling the obligation refers specifically to recounting and explaining the significance of these things, or if it only pertains to not fulfilling the obligation of properly narrating the story of the Exodus from Egypt. The commentary of the Meiri (Pesachim there) suggests that Rabban Gamliel meant that one must not merely recite these elements, but also explain their significance in order to fulfill the obligation properly. The three things referred to are the Passover sacrifice, the matzah, and the bitter herbs, with each having a corresponding verse to emphasize their importance.

The Meiri holds that the recitation of these elements serves as a condition for fulfilling the commandment of recounting the Exodus from Egypt.

Similarly, the Shulchan Aruch HaRav (Siman Reish) explains that these three elements form the foundation of the obligation of the Haggadah, stating that when they are presented before you, it is for this purpose.

Rashi's commentary (Sefer Haorah Siman Pey-Tet) also implies that these elements are part of the obligation to sing and praise during the Passover Seder.

The Shelah (Pesachim Matzah Asirah - Drush Rishon) also explains that mentioning the Exodus from Egypt is essential. He emphasizes the praise for one who elaborates on the telling of the story by mentioning the Passover sacrifice, matzah, and bitter herbs. The Shelah notes that the emphasis is on reciting and narrating these elements rather than performing them, highlighting the importance of storytelling and recitation in the context of the Passover sacrifices and laws.

The opinions of the Rambam are also discussed by the Gra (Chiddushim to Masechet Pesachim 16:1), who explains the Rambam's statement that one who does not mention these three things on the eve of the fifteenth of Nisan has not fulfilled his obligation. The Gra concludes that all three of these distinctions are considered part of the Haggadah, and are included in the mitzvah of "And you shall tell your child" as part of the obligation of recounting the story. Since the mitzvah requires intention, one must focus on fulfilling the mitzvah through these three elements.