A. One view is that a scribe would hold his papyrus in his left hand and use his right hand, which with most people is the stronger hand, to write each line. Since Semitic tongues antedated Greek, Latin and the European languages, this meant that the original style of writing went from right to left.
However, we are still left with the problem of why the left-to-right method developed. The answer may be that there was no fixed custom and people wrote both ways, starting, say, from right to left and continuing with the next line from left to right, until eventually two styles settled down, with some languages going one way and others going the other.