My psychologist recommended a podcast about DBT to me, and recently I listened to an episode about shame and guilt. They were describing guilt as an emotion that helps us to connect with people, especially when we have hurt people with our actions, and how guilt can help us to be accountable/heal/repair relationships. Guilt is 'I've done things that are against my moral values'. On the other hand, they were describing shame as disconnecting and corrosive, when shame is 'I'm bad, I'm a bad person' which is quite a reductive, black and white way to process. And even though guilt can be a more helpful difficult emotion, it can be much easier to feel shame instead. In my experience, it's harder to apologise from a place of shame because the only thing you're admitting is 'yes I am a terrible person'. Which is rarely true, people aren't straightforwardly bad or good.
Although granted repeated behaviour does suggest some people are indeed really not very nice....but anyway, I do think that for an honest apology you need to be able to acknowledge what you have done (and care about what you've done?). Rather than being mired in shame/in the 'you think I'm a BAD PERSON' mindset. And the way Jack retaliates/reacts seems more like that to me. Plus when you're in a hole of your own self-righteous indignation, quite hard to pull yourself out of that.