I'm puzzled that she's saying she feels you're avoiding. Yes, some survivors both want to "go there" and to avoid it at all costs - that's the nature of trauma, isn't it?

I'm wondering if she's aware that maybe your (supposed) avoidance comes from her subtle inconsistencies, and I wonder if she examines her role in it, if any.

Yes, some of it could be your perception (for example, when my T gets firm with her voice tone, I always feel scared like she's scolding me even though we've worked together a long time), but someone telling you "I'm a safe person" is just words, and does nothing on it's own to convey safety. It's going to be how she is as a therapist/person over time and with consistency that will show your nervous system whether or not she's safe enough or not.

When she said she feels there's an element of avoidance, how did she say it? Did she seem to blame you? Or did she say stuff where you feel that given more rapport/trust over time, you could open up to her?

I hope that she'll prove trustworthy and helpful. Or if not, that you can find the therapist you need.