I'm so sorry for you. I've had a depression and my partner has recurring depressions, so I understand what he describes about his unability to feel. However, it's so important to not make (important) decisions while your in this state. You can't think clearly. Life's miserable already, who cares if I give up everything etc. He probably doesn't realize that now, but it's really important. It will make him feel even more miserable if he pushes everyone away and makes sure he has nobody around him who cares about him. I hope you or someone else can tell him this and that it will sink in.
I understand his feelings about professionals. My partner and I never have been helped by professionals either, but still he really shouldn't give up. You have each other and maybe you can get help, so you can get advice how to talk about it with him. Or maybe some other kind of coach or physical therapy if that is easier accessible for him.
If he's already feeling really bad, why should he break up with you? What for positive things would give him this in return? You are more hurt when he leaves you, than when you go through this with him. So he shouldn't think that this would be better for you (that's what I often think).