It may be that your T is simply encouraging you to continue because she understands you have some avoidance?

That said, I do also think that a good T will have a tendency to emotional involvement. I myself have lived a life quite detached from my emotions, from the way my T talks I can see that being in touch with her emotions is part of her being, for her being human is to feel her feelings and I think she is emotionally involved with her clients in a healthy way, I'm sure she processes it in her supervision.