Final answer:
General Lee crossed into Maryland and fought the Battle of Antietam to win a decisive victory on Northern soil.
Step-by-step explanation:
The reason General Lee crossed into Maryland and fought the Battle of Antietam was to win a decisive victory on Northern soil. The Confederacy wanted to show their strength and gain momentum by winning a major battle in Union territory. By doing so, they hoped to force the Union to negotiate a peace treaty and end the war.