Part of the answer is that the Eastern Mediterranean already had a well-established lingua franca in koine Greek, a transnational dialect of Greek spoken in the areas conquered by Alexander the Great and ruled by his successors, who used it as their administrative language, as well as the language of high culture, and a necessity for mobile individuals like merchants. Mind you, people still generally spoke native languages, including Demotic in Egypt and Aramaic across much of the Levant (notably the Jesus' native language). Indeed, the entire reason the New Testament was written in koine Greek, rather than Hebrew or Aramaic, was precisely because this was the language that had the most reach.

There was no similar lingua Franca in the western Mediterranean prior to the Roman conquests, although Punic probably was the most widespread major language. The spread of Latin in the west was promoted not only by Roman administration, but critically by massive colonization under Caesar, the triumvirs and Augustus, when hundreds of thousands of discharged soldiers were settled. Most Roman colonists during this period settled in Spain, Gaul, North Africa and Illyria. There was some colonization in the east, including the refoundation of Corinth in 46 and a major veterans' settlement in Beruit, but in the east these efforts were far less in scope and scale. While places like Corinth had a Latin speaking population (attested by Latin inscriptions), it was largely subsumed by the sea of Greekness.

Meanwhile, in the west, the prestige of Latin as an administrative language, coupled with the infusion of thousands of Latin speaking colonists, produced the conditions for the eventual deep penetration of Latin. The process was undoubtedly complex, and the shifting orientations of elites in the western provinces (who were more fragmented and more recently disrupted by war and conquest than their counterparts in the Greek east) no doubt also plays a considerable role in the story. The process was not rapid; Punic endured in North Africa for centuries, as did Celtic dialects in Gaul; Augustine was aware of vestigial Punic even in the 5th century AD.