To add to the question most religions of the time saw the left hand as a bad thing, so I’m assuming everyone regardless of dominance used their right hand. Also, wouldn’t the writing from right-to-left cause smudge errors in the script similar to how lefties get the “grey palm” when writing?
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Through different lineages, Arabic, Hebrew as well as Latin and Greek scripts ultimately come from the Phoenician script which was written horizontally from right to left (the first to have this kind of fixed direction). So the answer is just that Arabic and Hebrew ultimately maintained this characteristic from the parent script.
Greek/Latin on the other hand were still being written in a [boustrophedon](https://en.m.wikipedia.org/wiki/Boustrophedon) style: starting from the right to the left for the first line, then you start from left to right for the next line, with the letters flipped, and so on, giving a serpent-like way of writing. Ultimately Greek and then Latin had their direction codified as left to right only, and therefore maintained the flipped letter which became the alphabet we know today.
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