The fundamental flaw is not the arrogance of the claim, troublesome as it is, but that the claim requires that there was a Divine chooser who made a choice.
Halakhah is in the doing, and our ability to pass that practice down to the next Jewish generation depends on whether or not we can give it the significance it had for the lives of our ancestors.
The sense of peoplehood is the awareness that an individual has of being a
member of a group that is known, both by its own members and by outsiders,
as a people. (Mordecai Kaplan, The Future of the American Jew)