New Testament was written in Greek. But Jesus lived in Israel and was supposed to be the next King of Israel. I think it is probably fair to assume that he and his twelve apostles spoke Hebrew. Then why would the New Testament be written in Greek? I would think at least the Gospels part would be written in Hebrew.
First, actually, it was very likely that Jesus and His followers spoke no fewer than these three languages: Aramaic, Greek, and Hebrew. What language did Jesus speak?
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.
But why did they choose Greek? Well, first, we don't have the originals of any of the texts, but it is likely that most were written in Greek, however, there is some debate over a few of the books, just for your information.
The primary reason would be portability. Greek was a very wide-spread language. Hebrew and Aramaic were not. Further, after Peter had an encounter with Gentiles that had him declare that the message of Christ's resurrection was for the Gentile too, it became an international matter that all hear the Good News.
48 So he ordered that they [Gentiles] be baptized in the name of Jesus Christ. Acts 10:48
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.
"But Jesus lived in Israel and was supposed to be the next King of Israel. ... Then why would the new testament be written in Greek?"
There would be no special spiritual connection with Hebrew in particular; Christ did not come to reign over Israel. Christ is the King of Kings, and He rules over all the earth and heaven. He came for our salvation, to die a horrible death on the cross. His status as King of Israel was only "formally" recognized by Pilate, who had these words attached to the cross above Christ's head, in Hebrew, Latin, and Greek:
Iēsus Nazarēnus, Rēx Iūdaeōrum
Jesus the Nazarene, King of the Jews John 19:19-20
The authors of the New Testament were not really trying to write scripture. St Paul's letters were exactly that: letters that he sent to other diocese. For the most part, the various authors were simply telling what they had heard, or what had been passed down to them. Later, these works came to be recognized as scripture.
Greek was the language everyone spoke at the time. Even the Jews spoke Greek, and most Jews could not actually read Hebrew. The Letter to the Hebrews, directed to Jewish Christians, has Greek that "is in many ways the best in the New Testament". Matthew might have originally been written in Aramaic. Muslims might have a problem with something like the Koran not being written in Arabic (it is supposed to be the literal word of God). But Christians do not see a problem with the New Testament not having been written in Hebrew. It is the Gospel, not the language, that matters.
So major parts of the New Testament were written in Greek and not Hebrew because:
- Hebrew was not considered a "Sacred Language"
- The authors were not trying to write scripture
- Greek was (only incidentally) the most popular language of the time, so it turned out to be the primary language the authors used
The New Testament was written in Greek by Greek-speaking writers for a Greek-speaking, largely Gentile audience.
Paul was a Jew of the diaspora, and diaspora Jews used Greek in their everyday lives, with many of them unfamiliar with the Aramaic (or Hebrew) of Palestinian Jews. The development of the Septuagint is evidence of this language difference.
Tradition says that the New Testament gospels were written by Matthew, Mark, Luke and John, of whom three were Palestinian Jews. Ian Wilson says in Jesus, page 25, it can therefore come as quite a shock to discover that no-one can even be sure who wrote the gospels, and most scholars now agree that the authors were unlikely to have been disciples of Jesus. There is a strong consensus among scholars that Matthew and Luke were based on Mark's Gospel, and a lesser but still significant consensus that John was inspired by Luke's Gospel. A linguistic comparison of the gospels shows that they were derived from Mark in the Greek language.
If John was originally written in Greek, then the three Johannine epistles can be expected to have been written in Greek. The Book of Revelation was written on the Greek island of Patmos and appears to be addressed to churches in Greek-speaking Asia Minor, so naturally it was written in Greek.