I'm having a hard time responding because I feel like there is a big missing piece. Why not give him to someone that you don't know? You've explained that you don't know anyone that would take him in but not why you would not go to a shelter or rescue organization that you aren't familiar with.
Maybe it's an issue with shame? If you have a vet put D down, fewer people would be involved. You would not have to tell other people about how you feel you have failed your cat.
Maybe it has something to do with control? It might be that you feel like you have a lot of unanswered questions in your life and want a solution that is entirely knowable to you. If D is dead, you'll know what happened to him. Or maybe it brings back feelings of being entirely in someone else's control? If D goes to live with someone else, his fate would be entirely up to them. You wouldn't be able to do anything if something bad happened to him and that could remind you of something from your trauma.
Maybe it's an avoidance issue? Killing your cat doesn't seem like an obvious example of avoidance, but it would be quick and final. It might subconsciously seem like a way for you to not have to deal with everything that your cat has stirred up in you. It might also make picking the most drastic solution more appealing if it means that you won't have to invest more emotion and energy into the problem.
Maybe it's an issue with shame? If you have a vet put D down, fewer people would be involved. You would not have to tell other people about how you feel you have failed your cat.
Maybe it has something to do with control? It might be that you feel like you have a lot of unanswered questions in your life and want a solution that is entirely knowable to you. If D is dead, you'll know what happened to him. Or maybe it brings back feelings of being entirely in someone else's control? If D goes to live with someone else, his fate would be entirely up to them. You wouldn't be able to do anything if something bad happened to him and that could remind you of something from your trauma.
Maybe it's an avoidance issue? Killing your cat doesn't seem like an obvious example of avoidance, but it would be quick and final. It might subconsciously seem like a way for you to not have to deal with everything that your cat has stirred up in you. It might also make picking the most drastic solution more appealing if it means that you won't have to invest more emotion and energy into the problem.