The Gemara (Shabbos 21b) cites the dispute between Beis Shammai and Beis Hillel regarding what is the proper way to light the Menora. According to Beis Shammai, on the first night of Chanukah, one lights eight lights, on the second night one lights seven lights, on the third night six and so on. Beis Hillel holds the order is, one light on the first night, two on the second, and so on.
The Zera Shimshon explains their argument as follows:
The Beis Yosef asks, why do we commemorate the miracle of Chanukah for eight days when in reality the miracle only lasted seven days being that the flask of oil had enough oil to burn for one day. If so, the first day was not a miracle and there is no reason to remember it?
The Beis Yosef offers two answers. The first answer is that the Kohanim realized that it would take eight days to get new pure oil, and that they only had enough oil for one day. Therefore, on the first day they put one eighth of the oil from the flask into the cups of the Menora. The miracle was that this small amount of oil filled up the entire cup in the Menora and burned for the entire night. Thus, even the first day of Chanukah was a miracle.
The second answer the Beis Yosef gives is that the Kohanim placed all the oil from the flask in the Menora on the first night, and the miracle was that only an eighth of the oil burned, and this kept on happening for all eight nights. Therefore, even on the first night there was a miracle, since the Menora burned the whole night only using one eighth of the oil in the cup.
These two answers, explains the Zera Shimshon, are the source of the dispute between Beis Shammai and Beis Hillel. Beis Shammai holds that the Kohanim put the entire flask in the Menora on the first night, and from there, the oil got less and less with each passing night. Therefore, in order to commemorate the miracle in the way it happened, Beis Shammai holds that on the first night we must light eight lights and each subsequent night light one less light, to symbolize how the oil got less and less on each night.
Beis Hillel holds the exact opposite; that the miracle happened the first way the Beis Yosef described, namely, that the oil's volume increased each night after it was placed into the cups of the Menora. To commemorate this, Beis Hillel holds that we must add to the amount of lights that we light each night.
