The liturgy of Chanukah states that the Greeks wanted the Jews to forget "Your Torah and violate the decrees of Your will"; not the laws themselves, but their G‑dly aspect. Thus, the main set of laws that the Greeks opposed were "chukim", ones that have no logical explanation. These include the laws of ritual purity and impurity, the prohibition of mixing meat and dairy together, the prohibition of wearing a garment made of a combination of wool and linen, etc. The Greeks wanted these particular laws done away with and Chasidic philosophy explains that this is why the Greeks defiled the oil - in order to nullify the super-rational concept of purity and impurity.
Oil is compared to intellect….
Although the Greeks defiled all the utensils in the Holy Temple, the liturgy only mentions that "when the Greeks entered into the Holy Temple, they defiled all the oils of the Temple". This confirms that the Greeks put special emphasis on defiling the oil. It is also significant that the Greeks defiled the oil, rather than disposing of it. The key concept here is what oil symbolizes. Oil is compared to intellect; just as oil always rises to the top when mixed with another liquid, intellect is unique in that it can be objective by removing itself from emotions and rising above them. Emotions and the feeling of self are inseparable. Only intellect can rise above emotion and achieve an understanding which can even be contrary to what emotions believe. The intellect, ultimately, is able to change and control the emotions.
The Greek's goal was to attack the Jewish thought process by contaminating their intellect and ultimately causing the Jews to think like them. The contaminated intellect of the Greeks for the most part prevailed; indeed they succeeded in "defining the oil" in that many Jews became Hellenists, assimilating into Greek culture.
A Jew is always united with the essence of the Infinite G‑d….
Nevertheless, the Jew possesses something far deeper than intellect and indeed totally beyond it, the essence of his soul, known as the "Yechida". This is symbolized by the intact jar of pure olive oil sealed by the High Priest. On the level of Yechida, a Jew is always united with the essence of the Infinite G‑d, and nothing can interfere with this connection. When the Hasmoneans realized that the Greeks were seeking to destroy their attachment to G‑d, they awakened this part of their soul and exhibited self-sacrifice to preserve the essence of their religion.
Although the odds were against them in that they were a small minority even among their fellow Jews - let alone compared to the mighty Greek forces, they went forth to meet the enemy, even though logically it was inconceivable that they would win. Their self-sacrifice, which stems from the level of Yechida, elicited from G‑d supernatural powers that made them victorious. Since, spiritually speaking, the Jews aroused their Yechida - their "intact jar of pure olive oil sealed by the High Priest" - there was a corresponding physical manifestation in their discovery of the intact jar of oil sealed by the High Priest.
On the jar was written "with the seal of the High Priest", even though in order to be pure it is sufficient to have the seal of someone who is expert in the laws of ritual purity. The concept of it being sealed with the seal of the High Priest can be understood according to what the High Priest represents spiritually, as indicated by a scriptural verse referring to Aaron the High Priest as "holy of holies". (Chronicles I 23:13) Chasidic philosophy explains that the High Priest represents the highest level of self-nullification to G‑dliness reaching the level of self-sacrifice that transcends reason. (Sefer Hasichot 5750, vol. 1 Vayeishev) It was this power which was aroused and enabled the Macabees to succeed.
[Excerpted with permission from "The Jewish Holidays in Chasidic Philosophy".]