The meaning of a cat always licking the other's fur:
1. Kittens begin grooming themselves around 4 weeks old and will also groom each other with their siblings to exchange scents and strengthen their bond. This practice continues even as they grow older. Grooming each other is one of the most direct ways kittens express affection and friendship.
2. If you have multiple cats at home, you might sometimes find two cats grooming each other and suddenly starting to fight. One second they're full of affection, the next they're fiercely fighting. This is because cats will groom the one they perceive as weaker, seeing it as "needing to be cared for." Neither cat wants to be outdone, and both believe they are "the strongest," leading to the phenomenon of them fighting while grooming. 
The purpose of cats licking their fur
1. Keep skin clean. Cats have many protrusions on their tongues. Licking their fur removes old hair and tangled hairballs, as well as dirt and external parasites from their skin.
2. Regulating Sebum Secretion: Cats stimulate their sebaceous glands by licking their fur, thus regulating sebum secretion. The secreted sebum on a cat's fur has a waterproof effect, protecting the skin. Additionally, glands on a cat's face, the backs of its paws, the base of its tail, and around its anus secrete odor-emitting substances, which cats need to lick to spread throughout their body. For cats, scent is a matter of pride.
3. Regulating Body Temperature: Cats don't have sweat glands, so licking their fur in the summer causes saliva to evaporate, creating a cooling effect. This is also related to the fact that cats' ancestors originally lived in hot desert regions, and licking their fur to lower their body temperature was an essential activity for their survival.
4. Relieving Emotional Stress: Cats improve blood circulation in their skin by licking their fur, which helps relieve tension. For example, when they land awkwardly or anger their owner, a cat might suddenly start licking its fur to relax. It's incredibly cute and silly.
