A cat might be jumping with its back arched because it senses danger or threat. It tries to make itself look bigger and stronger to scare away its enemies. It raises the fur on its back and contracts the muscles on both sides of its body to form an arch, which increases its size and height, making the other party think it is not to be trifled with.
Or it could be because the cat heard unfamiliar sounds, saw something new, or sensed a change in its owner's emotions, creating an impulse that it uses to release its emotions and try to get its owner's attention.
