Studying to be a psychologist does not grant her compassion. She may even be exploiting him, or his benefits pension, who knows...

It sounds like the only thing left to do is to continue to try to convince him to reach out for help. You could point out that the people that he believes would be looking how to take advantage of him, simply have a job to do, that, that's their job to help people. May make it feel more like something he can live with. But in all likelhood, his refusals, whatever the rationale he gives, are part of his depression. He just doesn't want to be helped, just wants to get more and more miserable. But keep at him, encourage him, maybe one day may be somewhat brighter that he would decide that life could be worth living.

But also realize that you cannot make him want to reach out. You found yourself in this situation, and you care deeply and you are doing the best you can, but what you can do is limited, and that is not your fault.