Why did the Romans in the East speak Greek rather than Latin?

The Greek language spread throughout North Africa and the eastern Mediterranean after the conquest of Alexander the Great in the 4th century BC. After his death, his Empire was divided up and became kingdoms ruled by his Greek-speaking generals. These generals created Greek-speaking royal courts, where Greek-Macedonian culture was maintained.

When the Romans conquered these kingdoms, they made no attempt to change the official language to Latin. The Romans often admired the Greek culture, and many educated Romans and emperors studied Greek themselves. When the Roman Empire spread to western Europe, they found that most of the cultures did not have a written language. Latin was therefore adopted as the written language for bureauracy. This resulted in the local populations gradually also adopting Latin as a spoken language.