טעם למנהג אכילת מאכלים חלביים בחנוכה

1

רמא (או"ח תרע:ב) brings a יש אומרים (כל בו ור"ן) that one should eat cheese on חנוכה, because part of the נס was effected through יהודית who fed the enemy general cheese, thereby putting him to sleep and killing him.

Until now, we have seen that there is a מנהג to eat cheese as a direct זכר to what יהודית accomplished. לבוש, however, adds that the זכר is not specifically eating cheese, but rather falling asleep as a result of eating cheese.

2

All of the above is assuming that the aforementioned episode was contemporaneous to the גזירות preceding the נס חנוכה. However, בן איש חי [1] disagrees and says that this story was not connected to נס חנוכה. Rather, he offers a different reason to eat dairy, namely, that Antiochus outlawed [2] שבת,  ראש חודש, and ברית מילה. The first letter of חודש, the second letter of שבת and the third letter of מילה combine to spell חלב.

3

בני יששכר (מאמר ג סי' מב) offers a different reason, namely, that the Greeks wanted to eliminate observance of the תורה from כלל ישראל, so in that way חנוכה is like a new giving of the תורה, and just like on שבועות there is a מנהג to eat dairy, [3] so too on חנוכה.

[1] I was not able to figure out how to navigate a בן איש חי in order to locate this reference, however it is identified as being on page 44 by R. Abraham Chill in The Minhagim (Ktav 2018; chapter on חנוכה, last footnote).

[2] The purpose of outlawing ראש חודש would seem to have been that without קידוש החודש there would, by extension, be no ימים טובים.

[3] In greater detail, where משה רבינו went to שמים to receive the תורה, the מלאכים tried to keep it for themselves. One of משה's claims against them was that the מלאכים ate בשר בחלב at אברהם's home, so they were therefore no longer worthy of the תורה being theirs. אברהם in fact did so purposely, in order for משה to have this claim. This is (one reason) why we eat dairy on שבועות. Since נס חנוכה is כעין נתינת התורה, therefore 'ה orchestrated the נס חנוכה to be partly effected by dairy, resembling the original נתינת התורה.