In ancient times, writing was done by inscribing pictures on small, clay tablets with a pointed instrument. The first of these tablets were small enough to be held in the palm of the hand, and in this position, it was natural for the writer to make pictures one under the other, from top to bottom.
Eventually, however, the tables grew in length until they could no longer be held in the hand, but had to be laid among the forearm. In this position, the pictures that had previously been written from top to bottom were now most conveniently written from left to right.
By the time the pictures evolved into letters, the habit of left-to-right writing had become firmly established.