DC residents seek Statehood because it is the most appropriate mechanism to grant the US citizens who reside in the District of Columbia the full rights privileges of American citizenship. These rights would include not only full voting rights in the US House of Representatives and US Senate, but also full control over its own local affairs.
The United States is the only nation in the world with a representative, democratic constitution that denies voting representation in the national legislature to the citizens of the capital.
DC Government Resource Center: DC Statehood
Full statehood for D.C. could arguably be achieved by an act of Congress by exercising the powers granted by Article Four, Section 3 of the U.S. Constitution, although there is some debate about whether the consent of Maryland would be required.
Some aspects of the D.C. statehood agenda were achieved with the District of Columbia Home Rule Act, passed in 1973. Still more were encompassed in the District of Columbia Voting Rights Amendment, which passed Congress in 1978 but failed to be ratified by a sufficient number of states to become an amendment to the U.S. Constitution. The deadline for ratification of the D.C. Voting Rights Amendment passed on August 22, 1985.
Two years later, in 1980, local citizens passed an initiative calling for a constitutional convention for a new state. In 1982, voters ratified the constitution[1] of the state. Since that time, legislation to enact this proposed state constitution has routinely been introduced in Congress, but has never been passed.
"New Columbia" is the name of the proposed U.S. state that would be created by the admission of Washington, D.C. into the United States as the 51st state according to legislation offered starting in the 98th Congress in 1983 and routinely re-introduced in succeeding Congresses. The Congressional legislation was triggered by the provisional D.C. Statehood constitution that Washington, D.C. voters adopted in November 1982.
D.C. statehood movement - Wikipedia, the free encyclopedia
"New States may be admitted by the Congress into this Union; but no new States shall be formed or erected within the Jurisdiction of any other State; nor any State be formed by the Junction of two or more States, or parts of States, without the Consent of the Legislatures of the States concerned as well as of the Congress"
"To exercise exclusive legislation in all cases whatsoever, over such District (not exceeding ten miles [16.1 km] square) as may, by cession of particular states, and the acceptance of Congress, become the seat of the government of the United States, and to exercise like authority over all places purchased by the consent of the legislature of the state in which the same shall be, for the erection of forts, magazines, arsenals, dockyards, and other needful buildings"
It would appear that if D.C. actually wanted to become a state there are many problems with this. First it would need the consent of the Virginia and Maryland legislatures as D.C was originally established from land from those states. The other would be the issue posed in the constitution as to the purpose that this "federal district" is for. In order to change this, you would need IMHO a constitutional amendment that negates the establisment of both of those clauses in the constitution in order for D.C. to achieve statehood. The only problem you have with that is, then other states can use the same amendment to break themselves down geographically and then you have not only a 51st state but rather many more states. D.C. residents are represented locally, as well as nationally and know by living in a federal district what the restrictions of living there are.