A definition of "State" that equates "State" with "District of Columbia" turns the definition of "United States" into gibberish, because the definition then becomes a statement that "United States" "includes only the District of Columbia and the District of Columbia."
The definition of "State" includes the District of Columbia "where such construction is necessary to carry out the provisions of this title." What happens if the construction is not necessary? If "State" does not include the District of Columbia, then references to "states" in the Internal Revenue Code would apply to nothing at all. Which is absurd.
-from The Tax Protester FAQ
(Courtesy Sailor Tork.)