Because this is the dialect that Jesus and the disciples spoke at the time. They spoke in the Galilean dialect of Aramaic. So, this likely means the first Bible was also written in Aramaic before it was translated into languages like Greek and others. Remember, some of the most educated cultures then were Greece and Rome even though I think Rome had conquered Greece by then and Alexander the Great was hundreds of years into the past by the time of Jesus. Alexander the Great lived over 300 years before Jesus was even born.
Born: July 356 BC, Pella, Greece
Full name: Alexander III of Macedon
So, my wife was telling me how in Aramaic for example, it was debatable whether in translating whether Jesus walked "BY" the water or "On" the water in the first translations out of the Galilean dialect of Aramaic (likely into Greek). Why Greek? Likely because of the philosophical point of view of educated Greeks still at the time of Jesus. Just like today the educated Christian world still studies Buddhist philosophy then the Greeks would have been interested in Jesus' Christian philosophy. So, Greek (because of a more enlightened philosophic attitude in Greece historically then would have been "open minded enough" to be interested in Jesus and Christianity and less likely to kill Christians outright like Rome did with Lions in the entertainment arenas then.