You take half, and I’ll take the other half
ויקח מצה האמצעית ויבצענה לשתים ויתן חציה (הגדולה) לאחד מהמסובין לשומרה לאפיקומן ונותנים אותה תחת המפה וחציה השני ישים בין שתי השלימות
Take the middle matzah and split it into two. Give the (larger) half to one of those at the seder to guard it for the Afikoman, and they put it under a cloth. The second half place among the other two complete matzos
Many people have the custom to have three matzos on their seder plate. While there are practical reasons to have this number, there’s also symbolism in the number three. A famous explanation is that they represent the three forefathers: Avraham, Yitzchak, and Yaakov. The simple explanation behind this symbolism is that it was in the merit of the forefathers that the Jews were redeemed from Egypt. The part of the seder known as Yachatz is where we break the middle matzah and save the larger half for the Afikoman. Is there any connection behind this symbolism, and the fact that it’s specifically the middle matzah that is broken?
There’s an astounding story described in the gemarra, a rendition of a conversation that will take place in the end of days. Hashem will so-to-speak approach our forefather Avraham, and tell him: “Your children have sinned.” Avraham, uncharacteristically, will say: “Destroy them!” Hashem will say to Himself: “Avraham never really had a hard time raising kids. Let’s ask Yaakov, who struggled with childrearing. Maybe he’ll have mercy and pray for his descendants.” Hashem will tell Yaakov: “Your children have sinned.” Yaakov as well will respond: “Destroy them! They are sinners!” Hashem, will so-to-speak feel frustrated. He’ll say: “The old man Avraham doesn’t have reasoning, and the young Yaakov doesn’t have concern. Let’s see what Yitzchak has to say”.
Hashem will tell Yitzchak: “Your children have sinned.” Yitzchak will respond: “Master of the World, they’re my children? Are they not Your children? From the moment they said, ‘We will do’ before they said, ‘We will listen’ You called them ‘My firstborn son’ And now, they’re considered my children and not Yours? Further, how much could they really have sinned? How many years does the average person live? Seventy years? Take away the first twenty of those years, as a person is not held accountable in Heaven until they’re twenty. Of the remaining fifty, half of that is at night, when it’s not practical to sin. Of the remaining twenty-five, half of that is spent praying, eating, and relieving oneself.” Yitzchak concluded: “All that remains is twelve and a half years to sin. Hashem, if You can bear all of that, then great. If not, I’ll bear half myself, so long as You bear the other half. Even if You say that I have to bear all of it, behold, I offered myself to You on an altar.
We see from here that it will only be Yitzchak who will try to defend us in the end of days. In his merit, and due to his intervention, the Jews in the future will see Divine mercy and eternal redemption. Yitzchak’s winning argument will be that he bear half the Jews’ sins, and Hashem bear the other half. Perhaps, to hint to this future dialogue, we specifically break the middle matzah. This middle one is the one that represents Yitzchak. Half of it we keep for the Afikoman. In fact, we take the larger half for the Afikoman. Maybe when Hashem and Yitzchak divide up the sins of the Jews, it won’t be evenly split. If there were to be one half that is larger than the other, presumably Hashem would take the larger half upon Himself. This is symbolized by the larger half being reserved for the Afikoman, eaten at the end of the seder, which represents the ultimate redemption. That is to say, in the merit of our forefather Yitzchak, we will merit the ultimate redemption. May it come speedily in our days.
Chag Kasher VeSameach!
 Magen Avraham ad. loc. § 21, citing Sefer Maharil Seder HaHaggadah § 21 and Bach ad. loc. s.v. ומ”ש חציה
 Shulchan Aruch Orach Chaim 473:6, based on Pesachim 115b and Piskei Rosh Pesachim 10:30
 Shulchan Aruch loc. cit. § 4, based on Tosafos to Pesachim 116a s.v. מה and Piskei Rosh loc. cit., amongst others. Cf. Biur HaGra ad. loc. § 11, who rules like the Rif Pesachim 25b and Mishneh Torah Hilchos Chametz UMatzah 8:6, who say to have two matzos on the seder plate. He notes this is also the opinion of Rav Menachem Minyoni, cited in Tosafos loc. cit.
 Tosafos and Rosh loc. cit. say that you need lechem mishneh even on Yom Tov, so there needs to be two whole matzos at the time of the blessing. As well, Pesachim loc. cit. says that matzah is referred to as לחם עוני, poor mans’ bread (Deuteronomy 16:3), because it’s supposed to be eaten as a piece, and not whole. Therefore, one of the three is split in two, and the other two are (initially) left whole
 Ma’aseh Rokeach 16:58. Another famous explanation is that the three matzos represent the three categories of Jews: Kohen, Levi, and Yisroel. This comes from the teachings of the Arizal, written in Pri Eitz Chaim Sha’ar Chag HaMatzos Chapter 6, brought by the Ba’er Heitev ad. loc. § 8. For sure there are kabbalistic explanations for this, but see Shevet HaLevi 1:136 for a practical explanation. See also Aruch HaShulchan Orach Chaim 460:6
 Shemos Rabbah 15:4
 Shabbos 89b
 Exodus 24:7
 Ibid 4:22. This can’t be understood literally, as Hashem called them this while they were still in Egypt, and they said נעשה ונשמע after the Exodus. Perhaps since Hashem knew they would say this, they got this title even then
 Based on Psalms
 אין ב”ד של מעלה מענשין עד עשרים שנה. This idea also appears in Yerushalmi Bikkurim 2:1, brought by Tosafos to Moed Kattan 28a s.v. מה בחמשים; Yerushalmi Sanhedrin 11:5; Bereishis Rabbah 58:1, brought by Rashi to Genesis 23:1; Bamidbar Rabbah 18:4 and Midrash Tanchuma Korach § 5, brought by Rashi to Numbers 16:27. See also Torah Sheleimah to Genesis Chapter 3 § 202. For discussions on the ramifications of this concept, see Teshuvos Chacham Tzvi § 49 (and the Chida’s rebuttal in Nachal Kadumim Chayei Sarah), Noda B’Yehudah II Yoreh Deah § 164, Teshuvos Chasam Sofer Yoreh Deah § 155, Chavos Yair § 166, Pardes Yosef to Genesis 23:1, and Sichos Chochmah UMussar § 50 (from Rav Dovid Kronglass zt”l, mashgiach of Yeshivas Ner Yisroel)
 See Sanhedrin 107a which says all of the forefathers underwent tests, and Emes L’Yaakov to Genesis 27:12 understands that this dialogue will be Yitzchak’s test, as it goes against his inherent nature
 Rav Asher Weiss said this like it was a known idea. I only found it in Derashos Chasam Sofer II p. 306 col. 4 ד”ה כתיב, although it probably appears elsewhere