We've probably all seen a young child forced by their parents to apologize, only to deliver the sulkiest, shoe-staringest, least-sincere apology history has ever recorded. Clearly the child doesn't actually feel sorry. Actually feeling sorry takes reflection, a significant mental effort to put oneself in another person's shoes and understand how they feel. That's tough, and it's often bullshit -- that other person's shoes might suck.
"Do you store these in a bucket of warm piss, Gary?"
But actually feeling sorry is not the point of the forced public apology. It's at least in part a form of punishment, a public humiliation for the apologizer. Even if they aren't in the slightest bit sorry, seeing a bully stare at their shoes and hiss "Sorry" through clenched teeth is itself kind of fun.
Yeah, I'll bet you're sorry you got caught, you little rat-f**k bastard.