Fight, that conversation is going to get you nowhere. He doesn't care about your feelings at all. I think you keep expecting things of him that he just isn't capable of now.
I wouldn't have even mentioned the stutter. I'd take S to the doctor, keep note of it, and only tell him if there was some impact of when he was alone with S (like Dr wants a record of each time it occurs and circumstances or something).
I feel like you are trying to get him to parent and he just isn't there.
