Antietam Aftermath

Confederate General Robert E. Lee's army pulls away from Antietam Creek, near Sharpsburg, Maryland. The day before, Lee's force had engaged in the bloodiest single days battle of the war against the army of General George B. McClellan. The armies stalemated, but the momentousness of losses forced Lee to abandon his invasion of Maryland.
The important facts to be perused here is not Lees withdrawal, but McClellan's lack of pursuit.
Lee fell to a defensive position with 42,000 to 43,000 troops. McClellan had at least 50,000 troops at hand with many more in immediate reserve and moving towards his relief.
Lee was highly vulnerable. His army had its back to the Potomac River. A quarter of his force had been lost in the battle and his men were tired.
On September 18th McClellan received an additional 12,000 troops, and as many as 24,000 more were in a position to rapidly deploy to relief if needed.
Although he outnumbered Lee's troops by almost three times, McClellan did not pursue the cagy southern general. McClellan overestimated the size of Lee's force. He erroneously assumed that Lee had nearly 100,000 troops in his command. The fall of Harpers Ferry Virginia on September 15th convinced McClellan that Lee had far more troops than actually existed.

It should be noted that McClellan’s soldiers were extremely fatigued after the Battle of Antietam. It would be difficult to rally them for another attack; but with the proper intelligence of Lee’s forces and successful delegation of fresh troops at hand the task of aggressively pursuing Lee’s army could have significantly hastened the end of hostilities.
Instead, Lee was allowed to escape across the Potomac. A chance to destroy the Confederate Army of Northern Virginia was lost, and the war lasted another two and a half years.