That's how the original alphebet-the Proto-orthanography that developed into the Hebrew, Arabic, Greek and Latin alphabets- originally was, you know :) ?
The 'Latin' alphabet that you are now using was, at one time, written right to left by the Phonecians (who could be pretty much anyone living east of Greece at the time...). These were an eastern People, who's alphabet was preserved in many Eastern languages (in a more intact form).The Greeks took it up, altering some symbols, using some symbols that refered to non-native Greek sounds for vowels (the original alphabet had diacritics for this purpose, so does Hebrew, but the phonological/morphological structure of Greek does not facilitate this), and eventually used a process called boustrophedon (refering to the back-and-forth movements of plowing a field) to read from right to left, left to right, then right to left. This is still evident in very early Greek texts. Eventually, this hardened into a pure left-to-right style of writing. The Etruscans living in Italy adopted the Greek alphabet (both they and the Greeks were in contact for a while-the Greeks pretty much lived on the whole of South Italy, Magna Graecia, before the Romans took over), made their own alterations. They then passed the baton to the Romans (one of many Etruscan traditions to go to the Romans-others included the toga and gladiatorial practices), who, several steps later, sent it to Germanic languages. Germanic peoples added runes, took them away, tinkered with the alphebet, got conquered by the Normans (who added to it), drove the Normans out, and somehow got the current alphebet we are using out of it.
So, the Hebrew alphabet reads that way because it is more conservative than the one we are now using.