I wasn't even aware that talking about self-harming to your T could lead to hospitalization. Is this only a thing in certain areas? My Ts certainly never threatened hospitalization for talking about SH.

I honestly don't even remember how I told my former T about my self-harming (my current T already knew about it from my file). I'd been trying to talk about it for a while, and then we spent a session with me getting as far as telling her that I had something to tell her that I felt was important, but it was really hard for me to talk about. The session after that was when we talked about it directly, and I don't remember what exactly I said, but I know that she hardly even reacted, and was quick to reassure me that she understood and that everything was fine between us.

EDIT: Thinking back, I might have said something along the lines of how I had struggled with coping with my emotions in the past, and how I had a history of self-harm. I think that might have been what got the conversation going.