Final answer:
President Lincoln had several reasons for continuing the war: military advantage, diplomatic considerations, and the desire to permanently end slavery.
Step-by-step explanation:
During the Civil War, President Lincoln believed that continuing the war was necessary for several reasons. One reason was the military advantage - freeing slaves would weaken the South's ability to fight since slaves were used as labor. Additionally, by embracing emancipation, the Union would have the opportunity to recruit African Americans as soldiers, increasing the manpower of the Union army. Another consideration was diplomacy - if the Union included the eradication of slavery in their cause, it would make British recognition of the Confederacy problematic, as the British public was anti-slavery. Lincoln hoped that proclaiming emancipation would also reenergize citizens who might support emancipation and enlistment of black soldiers, thus helping bring victory to the Union.
Another important factor in Lincoln's decision to continue the war was the long-term goal of permanently ending slavery. The Emancipation Proclamation, which was a wartime measure, only applied to Confederate territories and did not free all slaves. Therefore, Lincoln wanted to amend the Constitution with the Thirteenth Amendment to ensure the end of slavery in the entire United States.
In conclusion, Lincoln continued the war to gain military advantage, for diplomatic reasons, and to achieve the permanent end of slavery.