The question is what's underlying the machloket Beit Hillel and Beit Shamai on lighting candles? I know that the gemara says that Shamai goes according to sacrifices of Sukkot and Hillel goes "ma'alin bakodesh" but that seems like apples and oranges.
There are a number of explanations for the underlying Machlokes regarding how to light the Chanukah lights. We are including below one of the approaches that we wrote for the Insights to the Daf.
The commentators also discuss the connection between Sukos and the Chanukah lights. We are sending you what we wrote there. Others discuss the connection between the decreasing number of Parim on Sukos and how it represents the 70 nations (since there are a total of 70 Korbanos that are brought, like the 70 nations) decreasing in power over the Jewish people, while the lights of Chanukah represent the victory of the Jewish people over that foreign power.
6) CHANUKAH AND SUKKOS
QUESTION: The Gemara says that the reason for Beis Shamai's opinion that one lights Chanukah candles in regressive order (eight on the first night, seven on the second night, and so on), is because the number of cows that were brought as a Korban Musaf each day of Sukkos were also brought in descending numbers (thirteen the first day, twelve the second day, and so on). What do the lights of Chanukah have to do with the Korbanos of Sukkos?
(a) REBBI YEHONASAN M'LUNIL explains that on Chanukah, the Chashmonaim felt that the miracle of their triumph was greater than the miracle of Pesach. On Pesach, the physical existence of the Jews was threatened, but during the time of Chanukah, the spiritual existence of the Jews was threatened as well, because the Greeks wanted to obliterate all traces of the Jewish religion. Because of this, it was decided to make the holiday of Chanukah longer that that of Pesach. They therefore made it as long as the longest holiday in the Torah, which is Sukkos (8 days).
(b) According to "SEFER CHASHMONAIM" (one of the "Apocrypha," or non-sacred Kesuvim), the Chashmonaim were not able to observe Sukkos properly because of the war. Therefore, they made the Chanukah festival eight days long to make up for the lost days of Sukkos.
From Daf-Insights to Chagigah 12a
1) SPIRITUAL POTENTIAL, PHYSICAL ACTIONS, AND CHANUKAH
AGADAH: The Gemara records an argument between Beis Shamai and Beis Hillel with regard to what was created first, the heavens (Shamayim) or the earth (Aretz). Beis Shamai says that the Shamayim was created first. Beis Hillel says that the Aretz was created first.
This Machlokes reflects a fundamental difference in ideology between the two schools. Beis Shamai always looks at the potential inherent in the subject ("Ko'ach"), while Beis Hillel looks at what part of that potential is realized through actions in the physical world ("Po'el").
Beis Shamai considers the primary component of creation to be the potential that it contains, because the ability to do any act in this world comes from that potential, its Ruchniyus, or spiritual, energy. The source of all Ruchniyus is the Shamayim (from which the Neshamah originates), and therefore the Shamayim is the main part of creation and had to be created first.
Beis Hillel, though, maintains that the "Po'el," the actual execution of actions in the physical world, is the primary component of creation. This is because the world was created for the sake of enabling people to accomplish and perfect themselves in the physical world of Olam ha'Zeh. Therefore, Beis Hillel maintains that the Aretz was created first.
This difference in ideology is found in other disputes between Beis Shamai and Beis Hillel. In Shabbos (21b), Beis Shamai and Beis Hillel argue about how the Chanukah lights are to be kindled. Beis Shamai says that they are kindled in descending order, with eight lit on the first night, and one lit on the eighth night. Beis Hillel says that they are lit in ascending order, with one lit on the first night, and eight lit on the eighth night.
This dispute is based on this ideological difference. Beis Shamai maintains that the Ko'ach, or potential, is most important. Hence, on the first night of Chanukah, the oil that burned in the Menorah in the Beis ha'Mikdash not only contained the miracle for that night, but it also contained the potential to remain lit for the remaining seven nights. Since the oil contained the potential for eight days of miracles, we light that number of candles on the first night. Beis Hillel, on the other hand, maintains that the Po'el, the realization of the potential, is most important. Hence, on the first night of Chanukah, we only saw one actual miracle occur. By the eighth night, though, we had seen eight miracles occur.
Similarly, in Kesuvos (17a), Beis Shamai says that we praise the Kalah with whatever praiseworthy attributes that she has ("Kalah Kemos she'Hi"). This is because we praise her for her potential ability to attract a Chasan, which is measured based on the attributes inherent in her that are visible to the average person. Beis Hillel, though, says that we praise her with generous words of praise ("Kalah Na'ah v'Chasudah"), even though the average person does not see these attributes in her. This is because we look at what actually occurred: her Chasan was attracted to her, and he must have seen in her great cause for praise.
Also, we find that Beis Shamai and Beis Hillel argue concerning the text of the blessing over the flame on Motza'ei Shabbos. Beis Shamai says that the text is "she'Bara Ma'or ha'Esh," and Beis Hillel says that the text is "Borei Me'orei ha'Esh." Beis Shamai says that the blessing should be made on the original concept of fire that contained the potential for all future fires, and thus the blessing should be in the singular, "Me'or," since it is a single concept. Beis Hillel says that the blessing should be made on the physical fire that appears before us, which comes in many colors and may be referred to in the plural (see Berachos 52b).
(M. KORNFELD -- This approach is related to the approach presented in Insights to Berachos 52:2, in the name of the ROGATCHOVER GA'ON, in which the arguments between Beis Hillel and Beis Shamai reflect an ideological debate whether to place more emphasis on the Chomer [substance] or the Tzurah [essence] of an object. The Ga'on elaborates on this in TESHUVOS TZAFNAS PANE'ACH #50 and many other places -- see the Hesped of the compiler of the Teshuvos after Teshuvah #255, Rav Zevin's L'OR HA'HALACHAH, chapter on "Snow" footnote #11, Rav Kasher's introduction to TAFNAS PANE'ACH on the Torah, Bereishis, etc.)