Question

Why did he declare war on the southern states?

Answer 1

Lincoln did not declare war on the seceded states. As far as Lincoln was concerned, the Confederate States of America was not a separate nation at war but a section of the indivisible United States of America in rebellion. 

This may seem like just a semantic distinction but it had profound implications for the conduct of the war. 

If the CSA had been an independent sovereign nation, the seceded states would have to have been readmitted to the Union according to the processes defined in the Constitution. It would have acknowledged that there was a right to secession implicit in the Constitution, something the South claimed and the North just as vigorously denied. It would have left the door ajar to some future secession crisis and the prospect of another civil war. 

Many of Lincoln's novel interpretations of his Constitutional powers - his suspension of habeas corpus, the Emancipation Proclamation, his definition of conditions for readmission of the seceded states, his formation of militias and the later draft - were based on the argument that the USA was not in a war but dealing with a rebellion