Gee, cats are such clean animals, aren’t they? Always licking their fur and grooming themselves. They must really care about being sanitary, clean-cut pets…
Hmmm… that’s strange. Fluffy seems to groom himself a whole lot after you pet him. What, did you have some peanut butter on your fingers he has to get off? Maybe he’s allergic to your touch and licking it makes him feel better?
No, he’s most likely trying to get your stench off of him.
Cats have glands that are stimulated when they tug on their fur, that ooze their own scent. Licking the fur kicks those glands into high gear, making him smell more like himself and ridding him of the terrible, terrible stink of you. It’d be like if after every time you hugged your Mom, she immediately ran down the hall and took a shower.
Also, have you ever had a cat suddenly start peeing everywhere after you bring a new girl or guy home? Peeing on their clothes, or in the rooms they spend time in? It’s sort of the same principle, its trying to erase all signs of his or her scent from the area.