Was Alexander Great? [Lillian]

Why was Alexander “so great”? For centuries people have been saying Alexander Ⅲ of Macedonia was a great man, but why? After his father died, he took his spot as leader of the frightening Macedonian phalanx to then conquer Persia and took the throne of king Darius. When he got all of Persia him and his army went to go conquer more land killing roughly 100,000 enemy soldiers while doing it. 
So we all have to ask, Why should he be called great?Battle of Alexander versushttps://commons.wikimedia.org
He kills, He kills 100,000 enemies in the five battles he lead. If anyone should get the title great it should be someone who makes peace. The remaining 30,000 in number , he sold into slavery1. Whatever survives, he destroys it.
Why does he even want anymore land? Ever since he was born his parents educated him in academics and warfare. His father lead an army of formidable, Macedonian phalanx He has always been ready to lead an army. 
This progressed into him needing more land.
While on the hunt for more land he destroys many cities. One of the worst cases was Tyre. This island city refused to surrender to Alexander. After much fighting Alexander was losing men, so he decided to send his last soldiers on a manhunt killing everyone except those who went to hide in a temple. The survivors were sold as slaves and the great city… was now utterly destroyed 2.

Why Alexander, the power hungry conqueror, the man who killed and destroyed? Why great?