Thanks, Velvet. This is much more detailed but otherwise very similar to my T's explanation when I was confused about my own feelings for him. My feelings felt like a deep love in some ways, but I was very much aware of the fact that I knew him in only one context, in a boundaried, professional relationship, and therefore it was impossible to actually "love" him as a person, because I don't really know him as a person. We talked a lot about the confusion patients often experience between love and acceptance, and he said it's very common for patients who never had the security and love they needed from their parents to think they deeply love their therapist because the acceptance and compassion they receive from him feel like a deep love.
This article explains the process and the feelings very clearly, stressing the importance of talking about the feelings and learning from them rather than avoiding them or "fanning the flames." Handled properly, the growth and maturation process really does work exactly as this therapist describes it.