The historical setting of the New Testament is in the Roman Empire.
The Romans were enthralled with the culture, language and religion of the Greeks.
GREEK was the way educated people displayed their sophistication in the Roman Empire.
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While it is true that the Romans did speak a form of Latin known as vulgar Latin, it was quite different from the Classical Latin that we generally think of them speaking (Classical Latin is what we usually learn at University). Vulgar Latin is the language that the Romance languages (Italian, French, etc.) developed from. Classical Latin was used as an official language only. In addition, members of the Eastern Roman Empire were speaking Greek exclusively by the 4th century, and Greek had replaced Latin as the official language. (http://listverse.com/2008/05/05/top-10-myths-about-the-romans/)
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Early Christians were certainly strongly influenced by the Greek philosophers such as Socrates (the model for Jesus), Plato, and Aristotle.
Neo-Platonic academies, schools, and traveling teachers were everywhere.
Paul of Tarsus grew up in a hotbed of Greek culture and religious ideas.
The Hebrews/Jews had seen their culture and language smothered by the conquests of Alexander the Great. Greek subsumed Aramaic and Hebrew.
THE SEPTUAGINT was a GREEK translation of the OLD TESTAMENT.
What is beneficial about Greek?
The Greeks had a word for everything. The vocabulary was specific to a degree and depth Hebrew never was.