The Greek alphabet and all of its child systems such as Roman, Cyrillic, and Gothic are conventionally left-to-right writting systems. But why is that, considering it comes from the Phoenician alphabet, which is a right-to-left system?
Normally, you would expect a child system to follow its parent's essential traits, such as order, as Phoenician child's Aramaic (which is the parent of Hebrew and other arab right-to-left languages) does; however Greek is different. In this picture you can see the Greek alphabet (top hemisphere) and Aramaic (bottom hemisphere) — greek text doesn't go all the way to the right, aramaic doesn't go all the way to the left.
It seems this kind of change isn't uncommon, considering that the system from which Phoenician descends, ancient egyptian hieroglyphs, was actually left-to-right. So Greek's timeline roughly goes as
left-to-right (egypt) -> right-to-left (phoenician) -> left-to-right (ancient greek), staying as left-to-right until today (modern greek).
So, how do some languages just suddenly shift their writing order, and more especifically, how did it happen in Greek's case?