One of the lessons mother cats teach their kittens is how to recognize when someone is dangerous. The mother toys with a small animal, large insect, or one of the kittens, while the kittens watch. Then the mother turns her back to the prey, and just sits with her back to it, perhaps washing her paws. The kittens are watching, waiting to see what will happen. As long as the mother cat's back is turned to the prey, the prey is safe. Then she turns around to face the prey, and the battle is on again. The kittens have learned that a turned back means no attack.

I've seen my cats turn their back on other cats, on a vulture, and on a deer. It means no attack. "I will not attack you, so you have no reason to attack me." Turning their back is a way to communicate no attack.

I have used this to communicate with skittish stray cats-- I sit on the ground with my back to them, and they understand that I will not attack them. Then they feel safer with me and gradually approach.

Perhaps ignoring a cat is like turning your back to them; in fact it may include turning your back to them. Perhaps that communicates the no attack message. There will be no fight; you are not dangerous.

Source: QUORA