Aramaic was the primary language of the land, Greek was the language of business, education, and for communication with foreigners (because it was a wide-spread language), and Hebrew was the religious language of the Jews and was primarily reserved for prayers, religious teaching, and communication with other Jews.

The primary reason would be portability. Greek was a very wide-spread language. Hebrew and Aramaic were not.

Greek was the language that made sense. It was wide-spread, it was for the foreigner, and the Jew knew it as well. Greek was the language that would affect the most people.