What is Alexander's reason for leaving his homeland?

Assuming you are taking about Alexander the Great, Alexander had several reasons. Under his father, Philip, the Greek city states were unified. Alexander had dreams of becoming a conqueror sprouting from early childhood. After Philip's murder, Alexander set out to conqueror everything in his path. Alexander was taught by Aristotle, who showed him a map of the known world. Alexander was a fierce general and fierce leader, who sought world domination. Alexander was a man of culture, creating the Hellenistic (blend of Indian, Greek, Persian, African Egyptian cultures) Age in Greece. As technology was nowhere near what it is today, an Emperor or King would have to travel with his military in order to have latest news. It would take days or weeks for a runner or rider to relay information to the capitol, so it made the most sense for a king / general to be with the military. Alexander was beloved by his subjects and his military, but also showed no mercy to those who opposed him, even burning his own city and erasing all of its history when a few of the citizens organized a rebellion. It is pretty obvious why Alexander left Macedonia - he had to be on the front lines leading his men in conquest.