Domestic cats lick their coat where you have petted them because you have disturbed their coat and they want to put it back to the way it was, mainly in respect of removing the scent and oils deposited on it. The fur may also be disturbed and they want it to be as it was.
The alternative reason why cats lick where you pet them is because they want to taste your scent which you have deposited on their coat.
These are the two reasons why cats do this. Over a period of time, actually decades (!), I have come to the conclusion that the first reason is the correct one.
No doubt there will be many people who will disagree with me because this is a debatable topic. I don’t know of any studies carried out on it. It’s up for grabs as to what we think about it.
However, I believe that cats know how their coat feels. They are fastidious and they like their coats to be just the way they like it. They can sense how it feels and if it feels right. They can sense how it smells and if it smells right.
That said, cats do not always lick where you have petted them. Although it does happen very often. I can play around with my cat 20 minutes, petting him, squeezing him and kissing him to express my love and he does not bat an eyelid although he does close his eyes very slowly indicating that he likes it. But afterwards he does not lick his coat.
However, when he is on his cat condo soaking up the sun and snoozing and I come along and give him a kiss in the middle of his body he will always lick it afterwards. He likes me doing it but he also likes to have his coat just the way he likes it. Not everything that we do in expressing our fondness for our cats is appreciated. Cats sometimes irritate us and vice versa. I am not saying that cats are irritated when we pet them. They like it if it is done properly but I am generalizing. That’s my theory what yours?
There is a theory, now that I think about it, that says that cats don’t like being petted or certainly don’t like to be overpetted as it can be stressful. If this is true it supports my conclusion as to why cats lick their coat after being petted.
P.S. This is my second attempt at answering this question.