If I live in DC, and work in MD, why do I owe MD state tax?

No.  Your W2 should tell you which state taxes were withheld for (in box 15).  Since you live in DC, this should be DC and you then only need to file DC taxes.

"If you work in Maryland but reside in a reciprocal tax state (Pennsylvania, Virginia, West Virginia or Washington, D.C.), and your only income from a Maryland source is wages, you can be exempt from Maryland income tax and Maryland withholding tax on those wages."

Source: http://taxes.marylandtaxes.com/Individual_Taxes/Individual_Tax_Types/Income_Tax/Filing_Information/D...

Since you changed your resident state you will be filing a part-year return for DC and one for MD.  On the DC return you will be taxed for the portion of the MD wages paid while a resident in DC from 1/1 to 3/25 (83 days).  On the MD return you will be taxed on the wages from 3/25 to 12/31 (282 days).  Divide the income by 365 and multiply by the number of days in each respective state. 

Ideally, your W2 should show two state lines with wages and withholding for both MD and DC.  Enter the W2 just as it indicates.  You can adjust in the state interview if it is off.  If there was zero withholding for one of the states then you may owe taxes to that state when filing.  

In each state return you will be asked to allocate the income.   To generate the part-year returns indicate in the "My info" section that your resident state on 31 Dec was MD and you lived in another state (DC).  

If there has been no MD withholding be sure to submit a new state withholding form to get that started going forward.