Korach is the name of this week's Torah portion. It tells the story of a cousin of Moses who gathered 250 people and started a rebellion. This rebellion stemmed from Moses' divine mandate to appoint someone else as leader of the Kohathites (a group of Levites). This sparked Korach's anger and envy.
Now, the verse in the Torah that describes Korach's declaration of war, so to speak, says: "The whole congregation is holy, and God is in them, so why do they exalt themselves above the congregation of Hashem?" It seems like a valid complaint, however, it's clear from the verses and the Midrash that Korach wanted to be High Priest himself, indicating that he, too, was actually seeking to be "above" others... so why did he complain about the exaltation of Moses and Aaron?
One explanation is that, in reality, Koraj was proposing a different kind of life than the one Moshe and Aharon led and taught (in accordance, in turn, with what God himself commanded).
The Ethics of Our Fathers (Pirkei Avot) says: "Beloved is man who was created in the image of God, etc., Beloved is Israel (the Jewish people) who were called children of God, etc." From these words arise two very interesting points (which are commonly misinterpreted): regarding creation in the image of God, the text uses the word man, while regarding being called children of God, the text uses the word Israel.
This means that all human beings, that is, all the children of the First Man, were created in the image of God. There is a common denominator in all humanity. The Jewish people, moreover, possess other qualities that are expressed in practice as merits and responsibilities in the observance of Divine precepts (which in no way diminish the other peoples of the earth, but simply add, as we mentioned, merit and responsibility upon the Jewish people).
One might think that this added merit and responsibility applies only to the mitzvot and not to matters of daily life, such as eating, drinking, etc. This is precisely the basis of the argument between Korach and Moshe.
Korach argued that there is an inherent holiness in human beings, therefore there is no need to sanctify oneself and elevate oneself in the worldly affairs of life. God gave us mitzvot, let us fulfill them, but as for the rest of life, "why do you exalt yourselves above the congregation of Hashem?" "Everyone is holy," Korach argued.
Moshe, on the other hand, argued that while all human beings are holy and there is an additional merit and responsibility upon the Jewish people, one must also rise and sanctify oneself above the rest of the nations in everyday matters.
As Maimonides says in his book of laws (which means it's not just good advice, it's a law): "A wise man is recognized not only by his wisdom, but by the way he eats, drinks, walks, and conducts business.""
Jewish holiness should permeate all aspects of life, from the way one fulfills a Mitzvah to the way one speaks to one's spouse and children.
That is the ideal against which Korach rebelled. Of course, the narrative clearly shows that his way of thinking was neither appropriate nor what God desired. (It is worth mentioning that this discussion has a direct application, from another perspective, to the problem of assimilation, where Korach argued that all human beings should be and live in the same way, and Moses responded that this is not the case...).