I'm sure if you have lived with a cat, you are familiar with how often they clean themselves. For a creature that is so graceful and proud, it's always surprising when you see that your grooming-obsessed feline seems to frequently focus on licking parts of themselves that are not so... graceful. Specifically, that your cat licks their own butt. Why? What reason could a cat possibly want to lick themselves there?
Cats groom themselves regularly because grooming helps your cat stay healthy. It helps them stay cool in the summer since they cannot sweat like people do. In addition, it also maintains their fur health in the winter by spreading the natural oils their bodies produce that help trap heat. This means that their butt is not excluded from this self-maintenance, and since there is no such thing as kitty toilet paper, their only way to keep their butt clean is by licking.
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If you cat is incessantly licking their butt, or rubbing their backside along carpets and floors, this could be your kitty trying to relieve themselves of discomfort. Cat saliva has enzymes that act as natural antibiotics, so when they have cuts or infections, it's like putting kitty Neosporin on. This discomfort could be as small as little cut, or could come from being constipated, having an allergy or even an infection in their genital region. If you notice this or your cat spraying urine through the house, or licking themselves to the point of rawness, it would be best to take them to your vet. This way your veterinarian can check them out in case they have an ailment in their nether regions.
To protect from predators
Your cat may be a happy house cat now, but they still keep up practices from living in the wild. In nature, cats stay under the radar from predators by being hard to find and especially hard to smell. You cat cleans itself regularly to stay safe from predators trying to sniff them out by wiping away food, dirt, or anything else strong smelling. Sadly, most animals buttholes are probably their stinkiest part. So your cat keeping it clear of fecal residue is truly a matter of survival.
In case there's company
You might notice that your cat shows off their butt often. This is because among cats, showing your butt is a way of saying "hello, get to know me better." It's actually a very great compliment for a cat to offer another cat the option to smell their butt. Cats have an anal gland that gives other cats smelling it a great deal of information about who this cat is, reinforcing their social bond. Just like humans, first impressions make a difference and you want to put your best foot (or in this case, butt) forward. Your cat doesn't want to show off a dirty butt to someone they might meet or greet, so your cat might be frequently keeping it clean in case company stops by. Or just to show you, someone they like very much, their clean butt.
Overall, your cat is trying to feel their healthiest and look their best when they lick their own butt, as unappealing as it may be for the humans around them to witness. At the end of the day, you can take comfort in the fact that your cat is taking good care of themselves. However, if it seems to be obsessive or harmful to your cat, don't be afraid of checking with your vet, who will be able to offer help.