HardKnocks, I apologize that this is so long, but it's not a question I ever tried to answer with more than a few summary lines, and I had to think a lot about how to explain it.
For me, all remorse is deeply entwined with learning how to let go of control. I had to figure out why I was so deeply freaked out by situations of uncertainty where I didn't have power over the outcome. By separating my life into isolated chunks, I didn't expose myself completely in any direction. No one had "all of me," so no one could destroy all of me. In healthy people, that core protected area is occupied by genuine self esteem. They have faith that if other people fail them, they'll be ok with themselves. I didn't have that, so I set up a cheap substitute, a false version of myself that I imagined was stronger and more desirable than the real me.
The irony is that my method of protecting myself was what put me at genuine, rather than imagined, risk. My BH would have worked hard to keep our relationship together if I had been honest and straightforward about what scared me. Instead, I put a pin in us and started an A where I felt powerful and secure, believing I had the upper hand. In doing so, of course, I deliberately set in motion the potential loss of the person I was most afraid to lose.
A wayward's fears may not be obvious, and they don't have to be rational. The problem isn't the insecurities themselves, it's our unwillingness to admit them. WS are, in general, terrified of vulnerability. We can't bear to ask for things we might not get. We'd rather try to steal them from somewhere else to avoid risking rejection. I guess some WS might gloat over having the risk of exposure compartmentalized, like a pirate with treasure buried at every port. In my case, compartmentalizing helped with denial. By separating the A from my "real" life in my head, I protected my image of who I believed I was. I avoided admitting that I was a betrayer, a liar, and a cheat.
When I think about how I made that choice, thereby barreling towards my own destruction, I find myself empathizing with those unfortunate idiots who drank aquarium cleaner to protect themselves from the coronavirus. They were scared, they were arrogant, they acted impulsively, and one of them ended up dead. All they really had to do to be safe was stay home and wash their hands. But drinking that chemical made them feel powerful -- "I can prevent this, I'm smart, I'm doing something" -- and in their fear, that false sense of control was too enticing to pass up.
What helped me break that cycle? SI. Not any magic formula -- I wish I had one to give you, believe me -- but just writing here and exposing my ugly and shameful thought processes. I learned that the world didn't collapse because I exposed my darker side. People saw that I was weak and selfish and dishonest and all kinds of things I never wanted to face or admit about myself, and the world kept on turning. Some of the BS here will never feel anything but contempt for any WS, including me; I accepted their antipathy, and the world kept on turning. Best of all, some WS were people with good qualities, capable of being smart and kind, who admitted to those same idiotic, destructive fears, and were clearly better for it. They all said the only way through is to face yourself with brutal honesty. When I took that advice, it was agonizing, but I did not die of exposure.
Over time, I found members on both sides of the BS/WS divide who appreciated seeing a WW admitting to her faults and trying to grapple with them. That in itself was a dangerous moment in the process, TBH. Waywards sometimes try to substitute one form of self-gratification for another, and I had to be vigilant about not expecting ego kibbles for doing the work. And it's still rough to get busted down to size by 2x4s. I'm less wayward than I was, but 18 months is not long enough to rewire a 51 year old brain. That self-protective, even self-aggrandizing instinct is powerful. It will still allow me to lie to myself if I'm not careful, and that would be a big step towards allowing myself to lie to others again. I have to keep deliberately cracking my own shell.
As I did that, my self-perception gradually reunified with the reality of how I had chosen to live my life. I accepted that there were never multiple BraveSirRobins, cleverly managing an emotional empire, but one scared BSR manipulating levers behind a curtain, yelling that the Great and Powerful Oz Had Spoken. I was exceptionally lucky that my BH reacted to this with compassion. There are many BS who, understandably, walk away physically/emotionally when they discover they married a cheap fraud. It would be disingenuous to pretend that all stories like mine can have a happy ending.
Waywards know this, and there will always be some of us who value control more than the possibility of R. They'd rather go out in a blazing fight on their own terms than expose their underbelly and die with their guts spilling out. If you have someone who is hell bent on protecting their false self-image at all costs, I don't know how you ever get the growth from them that would allow you to build trust again. They aren't going to be safe until they learn to live with their own vulnerability.
My advice to your WS would be to accept that he's already fully exposed. He's not fooling you anymore. He's not fooling his IC. The time has come for him to face that the only person he has a shot at deceiving is himself. And in the long run, really, he's not even succeeding at that.