Have you been seeing the therapist long? Trust is a big deal for me (and probably lots of us) and I do feel turned off by anyone who wants sensitive info too fast. But also, this is how some therapists get at trauma...and it works for some people (the talk about details stuff), so I'm not discounting it. But I don't have access to several of my details or even the language because I was too young, too far unconscious (medical emergencies or really drunk), or some of it was less of an event I can recall and likely more connected to ongoing terror. So what I'm doing now is more Somatic Experiencing and body-oriented psychotherapy. It involves regulation, feeling okay in my body, finding a way to complete trauma responses (fight or flight) without having to go into details. For me, once something is sort of processed in my body or a dream, it is helpful to tell my therapist and we can talk, so it's not like anti-talk or details...it's just not the only way.
The few details I have threatened to put me over the edge and took well over a year to share. But then it wasn't so overwhelming and I had more tools in place to deal with it...vs initially not knowing what to do with overwhelm besides burn myself. If you are having trouble with symptoms, like self-harm or suicidal thoughts or just general functioning...all of that should be first in line. So hopefully your therapist could help you address ways to manage symptoms first, and know you have ways to tolerate working on trauma information.
Anyway, if you are feeling like you don't trust your therapist, maybe bring some questions about his/her goals or how the trauma therapy will work...and your concerns. Maybe the process can be slowed down. ? Or consider a therapist or form of therapy you might feel more comfortable with. It's important to trust your therapist, the process, and feel safe...however that will work for you, and your therapist should be willing/able to help you figure that out if you are not sure.