Cats have scent glands around anus and tail base. Facing butt toward you spreads pheromones marking "you're mine!"
Scent Glands
For some cats, backing up to your face is their version of a handshake when saying hello!
Greeting
Kitty may park their rear in your view to gain attention, treats or play time from you instead of meowing.
Attention Seeking
Exposing vulnerable rear areas demonstrates cats consider you part of family group and feel safe with intimacy.
Showing Trust
Painful defecation, worms, infections could cause cat butt displays prompting face investigation if area needs help.
Health Issue
Avoid startling sleeping cat with face full of butt. Let kitty make first move for consent on close contact.
Respect Space
Politely relocate cat instead of knee-jerk reaction to butt in face. Yelling or shoving erodes trust.
Respond Gently