We all know the Beis Yosef's question about why we celebrate eight days, when the miraculous long-burning oil only lasted seven days more than it normally would. The Aruch Hashulchan addresses this question in OC 670:5. He brings from the Sefer Chashmona'i that in the year before Matisyahu's rebellion, Antiochus had prevented the korban celebration of Sukkos and Shemini Atzeres. Therefore, when the Jews were able to re-inaugurate the Beis Hamikdash, they intentionally celebrated for eight days, in order to show that they were making up for the lost days of Sukkos and Shemini Atzeres. The eight days of burning, then, were simply a heavenly ratification of their decision to establish this eight day holiday. (This is actually made clear in the Megillas Chashmona'im.)
With this we can finally understand what Shammai means by saying that we should start with eight candles and go down one every day just as was done with the bulls that are brought on Sukkos. Everyone reading the Gemara is puzzled by this association, because this reverse progression is unique to Sukkos, and why would Chanuka davka reflect the singular rules of Sukkos? But now we understand that Chanuka was viewed as a stand-in, as a commemoration, of the Sukkos holiday and korbanos that they had been prevented from bringing.
This also explains why we find dinim of hiddur on Chanuka that we generally don't find in other dinim. The reason is, again, because Chanuka is, to some extent, a quasi-Sukkos, and Sukkos is a holiday when hiddur on the esrog and all the minim is stressed to an unusual extent.
Micha Berger of http://www.aishdas.org/asp/2006/11/chayei-sarah-kibbush-and-chizuq.shtml commented that he heard this association from Rav Aharon Soloveichik in 1993, and expanded on it with something else he heard from him. What follows is from Micha's website, Aspaqlaria, at the above link.
R. Chaim Soloveitchik holds that there is a distinct difference between the sanctity of Eretz Yisroel that came with the first commonwealth and that of the second.
The first Temple did not create a permanent qedushah (holiness). The reason given is “that which was acquired through conquering is lost through conquering. The First Commonwealth built on land acquired in the wars of the days of Yehoshua and the Shoftim (Judges), was itself conquered.
The Second Commonwealth was “merely” an immigration of a group of Jews who decided to live in the land as Jews. It is predicated on the mitzvos done there, the education of children raised there. That kind of sanctity can not be undone. “Qidshah lisha’atah viqidshah le’asid lavo – it was sanctified for its time and sanctified for all time to come”. Even today, Har Habayis (the Temple Mount) has the sanctity of the Temple.
R. Aharon understands his grandfather’s words in the light of this distinction. The first commonwealth was founded on kibbush. It therefore had an inherently inferior qedushah. The second commonwealth was built by chazaqah. When Hashem tells Zecharia, “Not by force and not by might but by My spirit”, He is saying that the second Temple should be build on chazaqah, not kibbush, to lead to a permanent sanctification. “Neqeivah tesoveiv gever.”
Rav Aharon Soloveitchik notes Chanukah’s connection to Sukkos. According to Seifer haMakabiim, on the first Chanukah people who had just missed being oleh regel, going up to the beis hamiqdash, with their esrog and lulav, did so then at their first opportunity. Beis Shammai taught that one should light 8 lights the first night of Chanukah, 7 the second, learning from the 70 bulls offered for the mussaf on Sukkos, which also declined in number each day: 14 the first day, 13 the second, etc… Rav Yosi bar Avin or R’ Yosi bar Zevida explains that Beis Shammai are emphasizing the link between Chanukah and Sukkos. (We follow Beis Hillel, and teach that the ideal is to increase as the holiday progresses. They do not deny the connection; but rather Beis Hillel asserts an overriding halachic principle — that we increase in holiness over time.)
The concept of being a geir vetoshav is at the center of the similarity between the two holidays. Sukkos is a time when the toshav leaves his home to experience geirus in the Sukkah. Chanukah is also about the ger’s Chazaqah, the rededication of the second Beis haMiqdash. Not about winning the war – the war wouldn’t be over for years – but about being able to live in Israel as Jews, with access to the beis hamiqdash.
My father taught Torah to thousands of Talmidim & Talmidos in numerous venues. Most recently in Stern College and Shulamis High School, where he primarily taught various classes in Tanach -- but has been teaching in numerous places for close to six decades. From Kiruv in JSS, NCSY, Torah Institute where there are dozens of familes of Shomrei Mitzvah today because of his influence, to Gemara classes to adults in Flatbush, Queens and elsewhere,to teaching at Esther Shoenfeld Bais Yaakov, Summers at Camp Morasha and the Morasha kollel, Night Seminaries, guests lectures and much more. He taught Talmidim & Talmidos, old & young, Gemara & Tanach, in a perfect Yiddish (Chasidish or Litvish), a Modern Hebrew, or a flawless English. He was simply a melamed Torah in its purest form. I rarely go anywhere where I don't meet someone who was his talmid.
Growing up on the lower East Side of NY he also had the zechus to interact with great gedoley Yisrael such as Rav Moshe Feinstein, Rav Henkin, Kapishnitser Rebbe ZT"L. He also had to do with the Ponovhizer Rav, various Amshinover Rebbes, Rav Dovid Lifshitz, the Lomzher Rav, Rav Zeidel Epstein, Rav YD Soloveitchik, Rav Mendel Zaks, ZT"L -- some of who were his Rabbeim.
Decades after it occurred he would relish telling over fascinating stories and interactions that he had with them -- remembering the details & the exact words & expressions they used.
Just one example of a story my father Rav Pesach Oratz hk"m had with Rav Moshe ZTVK"L.
My father was sitting & talking to Rav Moshe. Rav Moshe had his back to a full bookcase of Seforim & was facing my father. My father mentioned a sevara & Rav Moshe says "yeh, das iz a b'feirishi Rashba in Yevamais" (my father did Rav Moshe's accent perfectly). While saying this, Rav Moshe while still looking directly at my father sticks his hand behind him to the bookcase, without looking or turning around, pulls out a Rashba on Yevamos, puts his finger on a place, pulls it in front him & flips it open, all without looking(!!), and begins reading the Rashba flawlessly & seamlessly without having to look even a second for the place. My father sat there stunned and with his mouth open not believing.
This is the type of story he loved to share & retell. He loved Gedoley Yisrael.
Even more important is the hadracha he gave based on Gedoley Yisrael. During that same conversation Rav Moshe gave my father advice quoting a certain ma'amar Chazal. My father wanted to clarify or question & said "aber far vas etc." Rav Moshe immediately interjected & said "nein, oib Chazal zaggen azai is es azai". My father took that Mussar haskil on the Chashivus of a maamar Chazal with him the rest of his life.