The answer to this will depend on which cavalry wont it?
For reasons of physical decay, I have always got off using the left stirrup to lift myself clear of the saddle and then swung my leg over behind. This is similar to the Western dismount where the rider then steps straight down to the ground.
I dont. I bring my legs together, take the weight on my hands on the saddle, swing my left foot clear of the stirrup and drop to the ground.
A British army officer who became an RI later told me not to apologise. He said, I used the cavalry dismount. I got the idea at horseguards that the cavalry swing their legs over the back of the saddle and remain upright at attention hanging at the side of the horse, until the next order comes whereupon they all hit the ground simultaneously.
With respect to Esther and her superior historical knowledge, I never saw British cavalry dismount by swinging the leg over the neck of the horse nor turning their back towards the horse as the slide off. One must be facing one's horse. But Parade may be different from in a battle?
My understanding was the the cavalry dismount reverses the mounting of the horse. It avoids catching the sword and the front of the uniform (breast plate) on the horse or saddle. But the cavalry man must be able to clear the back of the saddle and any pack or bed roll fixed there.