They wanted all the slave states and were agitating to get them. That would have left Washington DC surrounded or in Confederate hands. No president was going to let that happen.
Wouldn't it be up to those states to do what they thought best for themselves?
Initially 8 remained in the Union while 7 left. It wasn't until Lincoln sought to use force against those seven that the others left, leaving 4 remaining (and creating a new one) that wanted to remain with the Union.
Of course some will argue that Missouri, Maryland and Kentucky were coerced to remain in the Union, so they didn't actually get to chose for themselves anyways.
That would have left Washington DC surrounded or in Confederate hands.
The location of Washington DC was chosen to be a compromise between the Northern power interests and the Southern power interests. Originally the Capitol was in New York, and the Virginians thought this gave Northern interests too much influence and so they wanted the Capitol moved to a more central location.
The Capitol physically left New York, but I now believe that the control New York had on it, never left the Capitol. We still see New York controlling the Capitol through their news lying system.