The three matzos of the seder are compared to Avraham, Yitzchak, and Yaakov (Maaseh Rokeach Seder Leil Pesach § 58). Why do we specifically break apart the middle matza (ויקח מצה האמצעית ויבצענה לשתים - Shulchan Aruch 473:6) symbolizing symbolizing Yitzchak?
The following is suggested by Rav Asher Weiss 1 al pi derush:
There’s an astounding story described in the gemarra 2, 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’ 3 You called them ‘My firstborn son’ 4 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 5? 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 6. 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 larger7 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 8. That is to say, in the merit of our forefather Yitzchak, we will merit the ultimate redemption. May it come speedily in our days.
1 Based on Minchas Asher Sichos Al HaMoadim Pesach s.v. פלגא עלי ופלגא עלך, said over in a shiur on the Arbah Kosos given in 5773 (found in https://www.torahbase.org/four-kosos-5773/ at the end)
 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
5 Based on Psalms 90:10
6 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
8 Magen Avraham 473:6 § 21, citing Sefer Maharil Seder HaHaggadah § 21 and Bach ad. loc. s.v. ומ"ש חציה
8 Rav Asher Weiss said this like it was a known idea. I only found it in Derashos Chasam Sofer II p. 306 col. 4 s.v. כתיב, although it probably appears elsewhere
Like you say, the middle matzah is associated with Yitzchok Avinu.
Kabbalisticly, Yitzchok is associated with the Kav of Gevurah and Judgement. This follows the idea that each of the three Avot correspond to one of the three Kavim. (Avraham to Chesed, Yitzchok to Gevurah and Yaacov to Tiferet)
Part of the Passover seder is related to the idea of Sweetening the Gevurot which is connected with the idea of redemption.
The breaking of the matzah associated with Yitzchok is part of that sweetening process.
This is similar to the idea of how Sarah Imanu's name was Sarai, spelled שרי originally. The letter Yud of her name was split in half into two Heh's. One she kept in her name and the other was added to Avram's name making him Avraham.
This change was done at the Covenant between the halves (Bereshit 15:10-14) which is also the time when G-d told Avraham about the Egyptian exile and the redemption from it.
It was this change that altered their destiny and made possible the conception and birth of Yitzchok Avinu. Redemption is also associated with the process of birth, like when the Jewish people passed through the Red Sea after departing Mitzrayim, similar to passing through the birth canal.
Each of those two halves of the split matzah correspond to our hands and feet which have five digits. The right hand is associated with kindness, which is why general Jewish practice is to begin all actions with our right. The left with Gevurah.
Gevurah is also the idea of division, like the five parts of the mouth which are the source for the pronunciation of the twenty-two different letters of the Aleph-Bet.
Some, including Chabad, also have the additional practice of breaking the larger of those two halves into five pieces which will ultimately serve as the Afikomen.