First, for the sake of clarity, I feel I should note that the asker of this question seems to be inaccurately conflating the scripts that are used to write languages with the languages themselves. The Greek language itself is not derived from the Phoenician language; the Greek alphabet is derived from the Phoenician alphabet. The language itself is not the same thing as the script that is used to write the language. For instance, English is its own language, but we write the language using the Latin alphabet.

Now, to answer the question, the earliest surviving inscriptions in the Greek language using the Greek alphabet are generally written from right-to-left, just like Phoenician. Throughout most of the Greek Archaic Period (lasted c. 800 – c. 490 BCE), though, the direction of writing in Greek was highly variable. Some inscriptions from this period are written right-to-left. Others are written from left-to-right. Many are written βουστροφηδόν (boustrophēdón), which literally means "like an ox turning [while plowing a field]." This refers to when the direction of writing alternates from one line to the next (i.e., one line written left to right, then one written right to left, then one written left to right again, right to left again, and so on).

Eventually, by the fifth century BCE, left-to-right seems to have become generally accepted as the standard direction of writing for Greek, but this wasn't at all a centralized process and some people continued to write right-to-left or boustrophedon even in the Classical Period.

There aren't really any surviving texts from this period that discuss direction of writing in any detail, but the most likely reason why the Greeks eventually settled on writing left-to-right is because, by the fifth century BCE, it was becoming more common for people to write using a wooden stylus on wax tablets or in ink on papyrus, whereas, for most of the Archaic Period, writing seems to have been mainly used for inscriptions.

Most people are right-handed and, when a right-handed person tries to write in wax or ink from right-to-left, their hand frequently tends to rest on top of the wax or ink as they write and smudge what they have already written. When a right-handed person writes in wax or ink from left-to-right, by contrast, their hand usually rests on the blank part of the tablet or papyrus and does not smudge what they have written. Thus, for a right-handed person, writing from left-to-right tends to be more practical. (This, unfortunately, creates a rather impractical situation for left-handed folks writing from left-to-right, who frequently have to worry about smudging what they have written.)