Because if you are unfamiliar with the horse it is easier to stop a potenitial runaway from a trot than from a canter.
FWIW almost all horses trained in sidesaddle know how to break from a walk to a canter so a horse can be taught to do so for a rider that requires/desires it elderly, disabled, ... etc.
I think it's just like a warm-up for humans, you walk first, then you jog, then you go faster, maybe?
I start with walking, then posting the trot on a loose rein. I can check for stiffness and unevenness at trot better then at canter. Then I canter around a bit both directions, in 2-point, still on a loose rein with my horse's nose to the ground, and THEN we can start the real work. Her trot is always MUCH better after we canter. She's forward, reaches into contact and her back is up.
That said, I've had instructors who has us warm-up at canter first. But I think that was just to decide who would stay on and who'd fall off and pay for drinks ;P