There are several reasons why cats like to chew on slippers:
Innate hunting instinct: Cats are natural hunters with a strong hunting instinct. Biting slippers may simply be the cat mimicking hunting behavior, treating the slippers as imaginary prey to bite and chase.
Curiosity and a desire to explore: Cats are naturally curious and full of interest in their surroundings. Slippers, as a common item in daily life, may pique their curiosity and desire to explore, leading them to use their mouths to examine the texture, shape, and smell of the slippers.

Relieving stress and anxiety: When cats feel stressed or anxious, they may chew on things to distract themselves and release tension. If a cat's living environment or daily routine changes, or if it lacks sufficient attention and companionship, it may seek comfort by chewing on slippers.
Oral health issues: Sometimes, cats chew on slippers because of oral discomfort or teething problems. If a cat's teeth are itchy or uncomfortable during growth, they may look for something to chew on to relieve the discomfort.