Generally speaking, when it comes to the Pesach Seder, people know the details of their own family’s practices but not those of many other families. From conversation, they might know what different people eat for maror but not necessarily when they stand and sit, how they engage in conversation, in what format they conduct the Seder. In an informal survey, I have found three ways in which families read the Maggid section of the Haggadah. In some families, only one person reads the text — the Seder leader, usually a grandfather or father — and everyone else listens quietly and follows along in the text. In other families, the Seder leader reads the whole text while everyone else reads along together quietly. And in some families, people take turns reading from the Haggadah.
While there are three contemporary practices, the Gemara seems to imply only one of them. When discussing whether a blind man is obligated to say the Haggadah, the Gemara (Pesachim 116b) says that they asked Rav Yosef’s students who recited the Haggadah in his home and the students answered that Rav Yosef said it, even though he was blind. He fulfilled the mitzvah for others, i.e. was motzi them (Rashbam, ad loc.; Tosafos, Megillah 19b, s.v. ve-Rabbi Yehudah).
This implies that it is proper for the Seder leader to read the text while everyone else follows along silently. And, indeed, the Vilna Gaon (Ma’aseh Rav 191) and Rav Shneur Zalman of Liadi (Shulchan Aruch Ha-Rav 473:24) say that one person reads the Haggadah and fulfills the mitzvah for everyone listening. Rav Shneur Zalman offers a reason for the practice. The general rule is “Be-rov am hadras melech,” it is better when people fulfill a mitzvah together than each individual doing it alone. For this reason, Rav Shneur Zalman says that it is best for the Seder leader to read for everyone and fulfill the obligation for them while they listen.
Rav Avigdor Nebenzahl (Yerushalayim Be-Mo’adeha, Pesach, pp. 56-57) notes a different practice, in which everyone reads along quietly with the leader. If it is clear from the Gemara, commentators and codes that it is best for one person to read the Haggadah, why would this other practice emerge?
Rav Yosef Karo (Beis Yosef, Orach Chaim 183) quotes Medieval authorities who say that with long blessings, it is best for each person to recite the blessings along with the leader. We see this with regard to the grace after meals (bentching) and the blessings on Shema. There are authorities who hold that even when one person says these out loud, it is best for everyone else to say the long blessings on their own so they can concentrate.
This would seem to be a good reason for everyone to read the Haggadah quietly with the Seder leader. Indeed, we find some authorities recommending this practice. Rav Shmuel Kamenetsky (Kovetz Halachos, Pesach 26:18) says that despite the implications of the Gemara and later authorities, it is best for everyone to read the Haggadah along with the leader, although he does not explain why. In footnote 21, the editor quotes Rav Yosef Shalom Elyashiv who likewise recommends that everyone read the Haggadah. Perhaps their reasoning follows the above logic.
III. The Important Parts
However, this was anticipated by the author of Seder Ke-Hilchaso (quoted in Ma’aseh Rav, Jerusalem 1987 edition, sec. 191 n. 17). He offers an important response to this objection. Blessings have many parts that if you miss any of them, you do not fulfill your obligation. The Haggadah is different. You can miss almost all of it, you can space out or doze off, and still fulfill your obligation. Some parts are required but very few. Therefore, it is easy to pay attention to the bare minimum of the Haggadah. (Rav Nebenzahl, ibid., adds that even according to this practice, everyone should say Hallel on their own.)
Perhaps this explanation also helps us understand the practice of those who take turns reading the Haggadah. If the reader fulfills the obligation for everyone, then it has to be one reader at a time. Different people can read different passages to which everyone listens. But there is another issue. There is a view that women have only a rabbinic obligation to read the Haggadah while men have a biblical obligation (see Pri Megadim, Eshel Avraham 479:2). While others disagree about women, everyone agrees that a child has at most a rabbinic obligation. How can a woman (according to some) and a child (according to all) fulfill the obligation of the men at the table by reading the Haggadah?
Based on the above answer, we can suggest that most parts of the Haggadah are not obligatory and if you miss them, you still fulfill your obligation. Therefore, perhaps it is best that a man (or the Seder leader) read the key Haggadah passages (Avadim Hayinu and Rabban Gamliel Hayah Omer) or that everyone read those passages quietly along with the main reader. (After writing this, I found that Rav Shlomo Zalman Auerbach say the same thing in Halichos Shlomo, Mo’adim, vol. 2, ch. 9, n. 214.)