In Leviticus 19, the text does not proclaim that the people ARE holy but that they SHOULD BE holy, that holiness is OBLIGATORY AND ASPIRATIONAL, an OUGHT, an ASYMPTOTIC IDEAL. But Korach's demand that Moses and Aaron share their power with the kahal, since "we are all holy," departs from this understanding of holiness. Indeed humans can never BE holy in the ontical or ontological sense that Korach asserts. Only God would be intrinsically holy in that sense. For the rest of us holiness is a matter of moral striving without end and an infinite task. Korach's claim that "we are all holy," misses all of this, as it aims (whether on behalf of Korach's own team or on behalf of all the community, if we take him at his word) at securing not a greater share of the responsibilities but of the spoils.
In a sense, Korach's misunderstanding of holiness as intrinsic to the kahal is the opposite of the misunderstanding of the spies (from last week's parshah) who saw themselves as "grasshoppers," as being utterly incapable of exercising moral or political agency, as intrinsically insignificant. The "truth" of the human condition and of human potentiality would lie somewhere in between the extravagant claims made by Korach and the feelings of extreme incapacity articulated by the spies, a truth that is most fully expressed in the words of Leviticus 19 in which it is not claimed that humans are holy but that they are capable of striving (and indeed obligated to strive) to be holy.
If there is a larger lesson for today in this, I think that it reminds us to be wary of all tacit or express claims of intrinsic superiority made by one group or another, as well as the obverse claims made about another group's supposedly intrinsic inferiority. Such claims and assumptions are expressed today in racism and ethnocentrism and in the more tacit claims of race, ethnocentric, or class privilege. No groups of human beings are intrinsically better than any other. As groups, and more especially as individuals, we each have the capacity to pursue good or to pursue evil, to seek after holiness or to do otherwise. Perhaps what the Torah comes to tell us in Leviticus 19 is that we are only human insofar as we understand ourselves as obligated to pursue ethical holiness as an ideal, which, at a minimum, means striving to treat one another justly and striving to elevate and never denigrate the humanity or personhood of the other.