They're trying to fool you into thinking their butt's are mirrors?
There are scent glands either side of that particular site, ones which cause cats to groom, in a major way. They don't think as we do, they have no idea that we aren't clued into their glandular communications. Rubbing their cheeks against us is marking us, with scent from alongside their mouths. The scent glands near the anus will cause a flurry of cleaning and grooming in a cats chemical world of reaction....
as for the butt in the face, i usually hiss and blow air really hard at them, at that instant.. it is frustrating to the cat and they will stop doing it after a few sessions of that reaction.
obviously, sometimes it is an invitation for mating, a sign you cat really really likes you. (the world of their brain is NOT the same as ours)
To them it is not gross, its just a way of communicating, they are offering you a sniff and a lick so you can understand them better, but also, they often do it unconsciously because it's no big deal to them where their butts are. It is disgusting and they can be taught not to do it, but it is no ill will from the cat.
Because they do that to eachother... cats sniffing each others butts are like when people say hello and shake hands... and they think it's just what one is to do when they come and greet you, like hey here you go have a sniff, you know it's me now.
That's how they say they love you.
I always thought that they think its a big laugh!
Coz they're superior+know us humans get offended+possibly find that rather amusing.Then we feed them,give them snuggles until next time.
"Where else would you like them to put it !!!