There is a known question asked by the Bais HaLevi and others: Why is it that only by Chanukah do we find that there is a basic mitzvah, mehadrin, and then mehadrin min hamehadrin?
The Bais HaLevi answers that, in truth, the whole nes of Chanukah only came about because the Bnei Yisrael were performing a mitzvah min hamehadrin.
The Bais HaLevi points out that there is no minimal shiur for the wicks of the menorah in the Bais HaMikdash. Normally, the wicks were spun to be somewhat thick, so that the flames produced would be full. However, halachically, there would have been no problem with making the wicks one-eighth of the normal thickness.
When the Bnei Yisrael found the pach shemen and realized that it would take them eight days to make more oil, they could have simply made the wicks during those eight days proportionately smaller and utilized the shemen available to them. However, they did not do so, because it would diminish the beauty of the mitzvah, and Hashem responded in kind and also gave them a “bonus” via the special nes of having the oil in the menorah last for eight days.
It is to commemorate this special mesirus nefesh to perform the mitzvah min hamehadrin that Chazal instituted that specifically on Chanukah, it should be possible to fulfill the mitzvah of lighting the menorah in a way that is considered mehadrin min hamehadrin.
The question still remains: Why, indeed, did the Bnei Yisrael decide to make the wicks the normal thickness come what may instead of using the (more rational) approach of making the wicks thinner?
Perhaps the answer can be found in the Sfas Emes. The Sfas Emes observes that the Gemara says that the ner maaravi of the menorah stayed lit much longer than the other neiros as testimony to everyone in the world that the Shechinah resides amongst Klal Yisrael. The Sfas Emes asks that, in truth, no one in the world could see the ner maaravi except for the kohanim doing the avodah. So what exactly is it testifying?
The answer, says the Sfas Emes, is the very fact that the Bnei Yisrael were privy to their own private nes in and of itself is testimony to the fact that they enjoy a special relationship with Hashem that the other nations do not have.
This, in fact, was the point of contention between the Yevanim and the Bnei Yisrael. Chazal say that the Yevanim made breaches in the Bais HaMikdash as if to show that anyone can enter, and the Bnei Yisrael are no different than anyone else. The Yevanim, so to speak, were trying to bring inside the contamination from the outside. That is why on Chanukah, we do just the opposite, and we purposely shine the light of kedushah that is found in a Jewish home towards reshus harabim to bring the kedushah that is found inside out in public.
When the Bnei Yisrael triumphed over the Yevanim, in essence it was a confirmation of the fact that we are different than the other nations of the world and that we do enjoy a special relationship with Hashem. If this was the victory that we were celebrating, then the Bnei Yisrael did not want to diminish the victory by then minimizing the very symbol of that victory. Therefore, they could not bring themselves to make the wicks of the menorah any smaller and, instead, purposely made them as always. Hashem agreed with this sentiment and brought about the nes of Chanukah. Our celebration of Chanuka with the mitzva of hadlakas neiros mehadrin min hamehadrin is a sign of the special relationship we enjoy with Hashem to this very day.