What are some reasons to say that Alexander the Great was great?
There are many reason to argue that Alexander the Great deserved his reputation for greatness. Let me name three of them.
First, Alexander the Great was arguably the greatest general that ever lived. He took a Greek army and marched into the heart of Persia and took over that empire. He even made it to India and conquered there. To do this as an invading army is even more impressive, because he was far from his home base. No other general in the ancient world can claim this much victory. No wonder he was the standard for all to follow.
Second, we can say that Alexander was great in his tolerance. For example, we can say that Alexander showed great freedoms to the conquered. For example, he respected the religions of all the conquered people. Polybius the Greek historian makes this point very clearly.
Finally, we can say that Alexander was great in his organizational skills and foresight. He intermarried his generals with the local population and sought to integrate people. His great marriages at Susa are famous. His desire to meld the elites of Greece and Asia was forward thinking.