I would definitely talk to your therapist about this. I think she would find it extremely interesting and exciting to discuss with you, not stupid.

HazelGirl mentioned projection, which is attributing to others things we have trouble with ourselves but I think it is more "reflection" which is seeing in others what we would like in ourselves or believe we see in ourselves. Therapists do try to "mirror" us so we can perhaps get an idea of what other's see when they look at us and I often deliberately recognize things I see in my therapist or others that I "want" for myself and copy them.

That doesn't necessarily mean that the other person is like you, just that your perception of them is like your perception of yourself at the moment. It's how we make friends sometimes, we see someone we are attracted to for something and, obviously, we like/want/have that something that is attracting us: the magnet and iron filing effect.