In those days, many were multi-lingual. Why not Greek? If it fit the purpose of their mission.
Jesus went to the Jews first and taught from their books and tried to reach them with the truth of who He (Jesus) was in the scriptures. Many didn't like what they heard.
There was no need for Aramaic, because the next people He was to share the truth with were the Gentiles. Greek would have been the best language to use to reach them with.