What is the reasoning behind Arduino choosing 9v?
You can actually supply 6-20 min-max (they don't recommend it though) and Arduino's recommendation is 7-12v.  One reason for this is because with the linear voltage regulator the arduino uses will have a voltage drop of around 2V and since the Arduino has been designed around 5V there is a ~7V minimum. The AVR micro controllers the Arduino uses can go below 5v, but not at the full clock speed. Some Arduino boards are 3.3v boards, and have different minimum and maximum voltages.

The reason the max recommended voltage is 12v is probably because any excess voltage will be let off as heat and the voltage regulator can only dissipate so much heat! You can operate the arduino from 5v, but you need to go around the voltage regulator.  That's how the arduino is powered from USB, which has a 5v line.