Washington D.C. has remained a district (as in the District of Columbia) rather than a fully incorporated state for a number of reasons. The main reason for DC’s lack of statehood is the same reason every state gets 2 senators regardless of population – our system is designed around maintaining the equality of power amongst states.
The founding fathers of the United States felt that by locating a national capital within a state that would give the state an unfair level of importance and prominence amongst the other states. While we no longer view the states in quite the same way as our founders once did, many of these rules still play a key role in our functioning.