Aramaic was the language Jesus and his disciples spoke; and it was the primary language of the Levant at the time. Why would the texts of a religion that originates from the Levant be written in Greek? A regular Jew or Syrian would not be able to read or understand Greek.
Greek was the Lingua Franca of the Roman Empire and most of the audience were Gentiles, not Jews. These books were all written to audiences living outside of Palestine, and most of them were written after the Jewish Holy Land had been destroyed. Most of the authors themselves do not seem to have known Aramaic or Hebrew because they all use the Septuagint as their Old Testament.