The reason ive always know it is the same a why seat backs have to be upright.
All equipment is designed to protect you in the event of a crash landing, you get the most protection when the equipment is in the correct, most stable position. ie seat backs up and armrests down. This is when the seat is at it strongest.
I dont know if it is the real reason but its what ive learnt, i dont use it to explain to pax who have their sleeping child, who they dont wanna wake up cause he will cry, lying across three seats. I uaully say if we have a heavy landing the arm rest is gonna come staright down on your child. they usually move the child pretty quick!