If the reason we light candles on Chanukah is as a commemoration for the fact that the lights of the menorah burned for 8 days on fuel that was only sufficient for 1, why don't we light our menorahs in the same way the menorah was lit in the beis hamikdash? Meaning, why don't we light all 8 (or, if we really wanted to emulate the way the menorah was lit, 7) candles each day of Chanukah?
The purpose of lighting is to publicise the miracle and not as a commemoration (in the sense of re-enactment) of the miracle of the oil. See Rashi on מבחוץ. Shabbos 21b .
Beis Shammai and Beis Hillel give different reasons for why they light in decreasing and increasing numbers of lights respectively.
The reasons are B”S – the days that are to come or the bull offerings of Sukkos (which decrease) and B”H – the days that have gone or because we increase in holiness and not decrease.
The reason for the changing number is not related directly to the miracle of the oil.
We purposely don't light a seven light Menorah because we aren't supposed to replicate the holy vessels for our own use.
The fact that we light for eight days shows the miracle of it lasting eight days. Nothing is to be gained by lighting eight candles. Therefore, the original Mitzvah is to light one candle each of the eight days. This means one candle per household.
The Gemara says that there are two levels of Mehadrin, of showing more enthusiasm about this commemoration and thanking of Hashem.
The first level is to add a candle for every person in the household. The next level is (according to Beis Hillel) to add one for each day. This shows how we are living along with the excitement of the fact that the miracle is for another day.
An alternative approach.
The answer to this question could depend on the answer to the question of the Beit Yosef as to why we celebrate Chanukah for eight days if we are celebrating the miracle (Shabbat 21b) that oil that should have lasted for only one day lasted for eight. We should celebrate Chanukah for seven days, since only seven days of the burning of the oil were miraculous!
The following two reasons (text taken from) (and) of the Beit Yosef himself might lead us to say that we increase the number of lights each day to symbolise our increasing wonder at the repetition of the miracle rather than lighting all 8 lights every day.
1) Those who were preparing the Menorah for lighting knew that it would take eight days until new oil could be obtained. They therefore divided the flask into eight parts, so that at least the Menorah would be lit every day, albeit not for the entire day. A miracle occurred and the small amount of oil that was placed in the Menorah each day lasted an entire day. Hence, there was a miracle on the first day as well.
2) On the first night, the contents of the flask were emptied into the Menorah. This would enable the Menorah to be lit for one entire day. However, after filling the Menorah, it was discovered that the flask miraculously was still full. This miracle repeatedly occurred for each of the days. Hence, there was a miracle on each of the eight days.
This does not seem to work for the first answer of the Beit Yosef that:
they split the supply they had into eight parts. Thus, on each of the eight days a miracle occurred, since oil that should have lasted for an eighth of a night lasted an entire night.
A full analysis of all the answers to the Beit Yosef's question is obviously needed.
A kabbalah interpretation from Rav Mansour 2009 Shabbat Drash
In the Beit Hamikdash the Menorah that was lit daily had seven lamps. So on the eight nights of Hanukah they lit a total of 56 lights . 7 candles per day for 8 days total 56) to nullify the (דין)
We also see in Tehilim perek 23 מזמור לדוד ה' רועי has 57 words to “sweeten” the .דין
There are 22 letters in the Hebrew Alphabet that correspond to (kindness). There are 5 letters that are סופי תיבות (the letters that words can only end with). They are מ,נ,צ,פ,ך these letters correspond to 5 דינים (strict judgement). This is seen in the fact that they “constrict” a word- disabling the word to continue after them. We see this alluded to in the וידוי prayer when we repent based on the מרדנו :are doubled (ex דינים-מנצפך The letters of .)אשמנו בגדנו( א,ב letters of the showing the strictness of these letters. The total numerical )מרינו דברך- נאצנו נאפנו .דינים 280 equal= 280. They are therefore called the מנצפך value of these letters Each one of the 5 סופי תיבות letters represents 56 out of the 280 (280 divided by 5 =56). So the number 56 corresponds to דין (strict judgment), this is why before ויהי נועם ה' אלקינו עלינו ומעשה ידינו כוננה עלינו :doing certain Mitzvot we say the Pasuk to sweeten the 5 times 56 contained )56=נו( s’"נו" 5 which has in it ומעשה ידינו כוננהו . דינים 280 in the In order to sweeten the 56 we “need” 57. The numerical value of the names of Hashem of ...'57= אל ה, so they sweeten the דינים of 56. That’s why it says in Tehilim א-ל ה' ויאר לנו that '57( אל ה) “lights up” לנו -the 56. The Greeks attacked us using 100 out of the 280 דינים. This is alluded to in the story of Yaakov’s fight against the angel of Eisav. The angel hit Yaakov in his כף- his thigh, the word כף is numerically 100, hinting that the שטן will “hit” the Jews with 100 דינים in the times of the יונים. The miracle of Hanukah was done with a פך שמן (a jug of oil). The word 100 and equals 100, hinting to the sweetening of the כף has the same letters as פך ,עשרת הדברות of the Greeks. This is also alluded to in the last letter of the דינים since there are 613 Mitzvot from the Torah and 7 from the Rabbis totaling 620. There are 620 letters in the עשרת הדברות, each letter corresponding to another Mitzvah.(an example of this is the first Mitzvah in the Torah which is פרו ורבו- to have children. The 552nd Mitzvah is to get married-קידושין the first letter in the from the word ל' and the 552nd letter is the, אנכי of the word א' is the עשרת הדברות This hints that in order to have a fruitful and successful marriage the couple .לא has to have the attitude of אנכי לא , there is no “I” in the marriage. No one can be selfish, a couple must always be considering the needs of their spouse.) The last Mitzvah is the Mitzvah of Hanukah, which is the final Mitzvah from רבנן. So the last letter of עשרת הדברות is the letter 'כ, alluding to the 100 דינים we overcome on Hanukah. (The letter 'כ spelled out is: כף which equals 100) So the extra day of Hanukah is celebrated to commemorate the overcoming of the 100 דינים, with which the יונים attacked us with.