because he issued the Emancipation Proclaimation that applied to slave states that left the Union. he wanted the border states to stay loyal to the Union and besides.... the border states never did secession anyways. hope this helps! :)
All the border states were in two minds about secession, but narrowly voted to stay in the Union. Lincoln made special efforts to keep them onside. He allowed Kentucky to remain neutral for the first year. And in Maryland, he (illegally) jailed pro-Confederate leaders.
The states that DID NOT secede from the Union was Delaware, Maryland, Kentucky, and Missouri. These four states did not secede from the Union because They were Border states, meaning they were between the Union and the Confederacy.