Why the New Testament was written in Greek
Hebrew was the language of the Jews while the Old Testament was being written. But during the Babylonian captivity, Chaldean, the language of the Babylonians, influenced Hebrew, resulting in a dialect known as Chaldee or Aramaic. By New Testament times, the Jews spoke and wrote both Hebrew and Aramaic, but they spoke Aramaic. Thus the Old Testament is written primarily in Hebrew with a few sections in Aramaic.
Between the close of the Old Testament and the birth of Christ, Alexander the Great swept through Palestine on his conquests. In his campaign to spread Greek culture to the world, he established Koine (or common) Greek as the language of trade. Even though Rome ruled the Mediterranean world during New Testament times, Greek was the “lingua franca”, the international written and spoken language.
Since most people understood Koine Greek, it was the language most suited to spreading the gospel message. The New Testament authors wrote in Greek to assure wider understanding, though they (and Jesus) most likely spoke in Aramaic.