This probably cannot be answered with certainty. One popular theory proposes that early writing was chiseled in stone. In order to carve letters into stone the writer would most likely use his stronger hand, which was usually the right, to use the hammer that would strike the chisel held in the left hand making the mark. Practically speaking it would be much easier to move from right to left. Maybe, maybe not? Many archaeological finds are inscriptions that were incised into wet clay instead of chiseled in stone. For instance, ceramic shards or clay tablets.
Ancient Jewish mystics, on the other hand, generally feel that writing from right to left occurred because the right side is given precedence in Judaism. Why is that? An ancient teaching assigns the characteristic of words ‘chesed’ (loving kindness) to the right side and ‘gevurah’ (severity) to the left side. Kindness always comes first and begins on the right. For this reason a scribe would be prone to start on the right and work towards the left.
As languages and writing instruments evolved technical issues could have changed writing direction. It is thought that as scribes used pen and parchment it was technically easier for them to write from left to right so that ink did not smudge. English definitely would have been one of the languages that moved in that direction while Hebrew and other Aramaic languages were already set with right to left movement.