I think that the "you" that President Lincoln invokes at the end of his Inaugural Address helps to bring out the idea that he does not wish to exacerbate the division in the nation. President Lincoln's primary focus in the speech is to preserve the union, not to antagonize the division already evident in it. The ending in which he uses the "you" helps to convey to Southerners that they, not he, hold the formula for resolving the growing conflict between North and South. Many in the South had claimed that Lincoln's purpose was to enter the south to remove slavery. They had constructed his election as one in which they had no choice but to consider separating. President Lincoln wishes to repudiate this in his speech. In using "you," he does as much, making it clear to the South that they hold the power in deescalating the conflict that has gripped the nation:
In your hands, my dissatisfied fellow-countrymen, and not in mine, is the momentous issue of civil war. The Government will not assail you. You can have no conflict without being yourselves the aggressors. You have no oath registered in heaven to destroy the Government, while I shall have the most solemn one to 'preserve, protect, and defend it.'
In this use of "you," President Lincoln wishes to suggest that the South can control how this conflict can be resolved. If war is to happen, he makes it clear through the use of "you" that it is something that the South will instigate and not something that he will initiate. Lincoln's use of "you" helps to construct a power element in which he makes clear that the South can take an active role in avoiding the bloodshed and division that might result from their incendiary words and actions.