So, why did Lincoln do it?
First, Lincoln balanced out the loss of white military support by picking up Black military support. And Blacks flocked to enlist. From their perspective they were fighting literally for their freedom. Indeed, they far preferred to die honorably fighting the evil of slavery than to die without honor in the heremetically-sealed grip of slavery.
This was true even though they were paid half the salary of their White counterparts, even though they were given the most menial of tasks, even though, when given a strictly military obective it was one doomed to failure – despite all that an estimated 186,000 Blacks joined the Union military. In other words that represented far more excited Blacks joining than disgusted Whites abandoning.