Most mammals (for instance, dogs) actually prolapse their anus slightly - they poke the inside part out a bit.
Cats, which don't prolapse their anus, have to lick the shit off their butthole.
Edit: More common questions answered here.
A) People didn't lick their buttholes before TP. They wipe with their hands, then lick those clean (or wash them). Some cultures do this in the modern day and age. Hey, at least they're washing their hands after using the bathroom (talking to you, guys in public washrooms). Personally, I consider it barbaric as fuck to use anything except a bidet.
B) Your dog rubbing his butt on the floor is actually a possible sign that he has worms. Take him to the vet, get him to check your dogs butthole. It's what he's paid for.
C) Yes, I watch a lot of animals poop. Like you don't.
D) Yes, you too can learn this skill. Have fun finding out how, though, or start a second thread. Preferably not in ELI5, as I would feel uncomfortable discussing that with a 5 year old.
E) Diet and posture while pooping can help, but let's not pretend you're going to actually change either of those things. Besides, if you DO learn to prolapse, eventually you'll be able to drop your bowels right down to the water and eliminate that nasty backsplash. Win/Win.
F) Pretty sure the cat tongue is sand-papery for multiple grooming purposes. Either that, or they want their oral sex to be like their PIV. Cats - spikes on everything fun. No wonder they're filled with hate.
G) I don't know why cats don't die from eating their own shit. I just assume it's because it's fresh, or that cats die from it all the time and yours just hasn't yet.
H) Yes, your cat is licking your face after licking it's butthole. That's okay, the Toxoplasm Gondii will make you feel alright about this. But seriously, don't let things lick your face, that's a vector for infection and honestly it's own butthole may be the least worst thing your cat has had in it's mouth.