My belief is that domestic cats lick fur instinctively by which I mean without conscious thought. It just happens. This goes against the grain of what we want to believe. You’d have thought that cats would have some conscious control over self-grooming and allogrooming (licking another cat). With respect to grooming another cat there is friendship a feline way but I’d argue that the act of grooming the other cat is instinctive
I made two videos. The first one, immediately below shows my cat licking the fur of another cat. I’m holding the other cat’s fur between my fingers. My cat instinctively licks the fur then sniffs it. He recognizes that it is not his fur but he still has an instinctive desire, despite his curiosity about the foreign scent from the fur, to lick it.
His licking serves no purpose. He must know that the fur does not belong to me because he can smell the scent of another cat on it. After I had finished videoing him he kept on searching for the fur even though I had put it away. He was searching for another cat.
I conclude, therefore, that feline licking is instinctive and a powerful motivator.
In the video below, at the base of the page, he is seen licking his own fur while I hold it between my fingers. He licked it all the time without hesitation. Once again there is no purpose because the fur is not on his body. I conclude, therefore, that once again his actions are instinctive and that is not making a conscious decision to lick this fur. In other words he is not asking himself whether he should or should not lick it. I have concluded that he does not think that he is licking me for the reason stated above.