While I've never found tea to have any particular calming or soothing effect it has frequently been suggested to me for precisely those purposes. Perhaps that is what your therapist uses it for? Kind of a self-soothing method... something they do for themselves during sessions to help themselves be able to tackle the difficult emotional work. If so, maybe that's why they don't think to share it with others, or are maybe even resistant to sharing it since it would no longer be a ritual that helps keep them separate/rooted in themselves?

Have you ever tried bringing your own tea in a travel mug to a session?