Most likely because medical students take lots of notes in class. They get a lot of information in a big hurry and have to write fast. They get into the habit of writing fast and it never leaves them. Also, on a prescritption, they use Latin abbreviations which the pharmacist understands but most people don't. For instance, t.i.d means ter in die, or "three times a day". PRN means pro re nata, or "as needed".
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