During the Civil War many blacks chose to fight for the Federal Army against the Confederacy. Black soldiers were discriminated against and at first restricted from combat. Later in the war the colored regiments saw some of the most extensive combat of the war. Thousands of blacks volunteered to fight to free their people from the horrors of slavery. Many of them were runaway slaves themselves, committed to end the system that had oppressed them all their lives. Many Black Americans felt that it was essential for them to participate in the war because, they wanted to end slavery, they wanted to support the whites that were dying for their people, and also to preserve the Union.
Probably the most obvious reason for Blacks fighting for The Union was to end slavery. By the time the war started both free Northern born blacks and especially runaway slaves, knew about the horrors of slavery. Naturally they would want to put an end to slavery in the south. Angry, vengeful runaways were probally the most determined and dangerous soldiers The North had. Given the opportunity I don't see why any runaway would not fight. The angry runaway portrayed by Denzel Washington is a perfect example of the disgruntled runaway.
Blacks may have in some way felt guilty that hundreds of thousands of white people were dying to save their people from slavery. As Morgan Freedmen's character points out, they were grateful for the whites fighting for them and wanted to do their part. Slavery may not have been the only reason for The Civil War but it was certainly enough to make blacks and whites alike stand up for what is right and moral.
Blacks like many of the whites were fighting to preserve The Union. The union had been protecting runaway slaves and all blacks from the evil clutches of the south. Northern educated blacks understood the necessity of preserving The Union. The nation could not be separate, because then the south would mistreat slaves even more, begin the importation of slaves again, runaway laws would be stricter, and new territories could potentially become slave states also.
In conclusion I think that blacks chose to fight because they wanted to end slavery, wanted to help the whites that were fighting for them, and to preserve the union. The nation was torn and both sides were dedicated to their cause, refusing to accept defeat. Among these I believe that blacks had the most to fight for and the most to potentially loose. It must have been every black man's dream to free his people from the chains of oppression.