The reason why a cat's back twitches:
1. When a cat is calcium deficient, it may experience unexplained trembling and twitching. The owner should supplement the cat with calcium in time.
2. If a cat swallows a foreign object and it gets stuck, it will twitch or convulse in pain. The object needs to be removed from the cat immediately. 
3. When a cat suffers from epilepsy, it may experience incontinence, frequent convulsions, and other symptoms, requiring immediate veterinary attention.
4. If a cat's diet is improper, such as eating raw, cold, or greasy food, it may cause indigestion, leading to reflux, vomiting, or gastrointestinal pain. It may also exhibit twitching or spasms, requiring immediate veterinary treatment.
5. Cats love to lick their fur. When hair accumulates and causes intestinal blockage, it can lead to back spasms. You can give your cat hairball remedy to help expel the hair.