I also think it's better to talk about these things, however, I just wanted to share my personal experience with counselling.
I told my counsellor I felt suicidal and she decided she should inform my doctor and involve social services because of the effect on my teen dd if I was to commit suicide - despite the fact I'd told her dd was the only thing stopping me from doing so.
It took a lot of talking to her manager to persuade her that I wasnt going to go through with it because of dd and to stop them involving others.
They do have an obligation to involve relevant professionals if they feel someone is at risk.
For years I hadn't told anyone how I felt because I was scared they would take my dd away, so to have them threaten to involve ss was terrible.
I've since not felt able to continue speaking to them as I didn't feel I'd be able to speak openly anymore. Luckily I found another organisation and a great counsellor but I think twice about what I say now.
I'm not saying you shouldn't talk to your therapist, just be aware that they have an obligation to involve who they think necessary if they think you or another is at risk.