carsan, I have to admit your post made me tear up a little bit, because I've been through this and a lot of what you said felt like it could be me.
What WePow said....it is a loss, and you truly are grieving, weird as it seems. It feels so strange, doesn't it? This person is still alive and well on this planet, but you cannot have any contact with them because of the rules of the unique therapeutic relationship. Coldly, clinically professional and yet brutally intimate and warm at the same time. It just isn't fair, is it? It's heartbreaking, a deep wound. It almost seems cruel, but the protection of the client is paramount. I keep telling myself that.
In 1999, I had a bit of a meltdown towards the end of high school and had to start seeing a psychologist. My diagnosis was social phobia. I was so shy and afraid of everyone and everything, I was so vulnerable. Not helping matters was the fact that I was graduating and was terrified of this life change. Our talks got serious pretty quickly. I thought about killing myself that summer (a few months into our work together), but that therapist helped me get through it and to stop the thoughts. I was able to go to college (community college) that fall. Well, right after Thanksgiving she dropped a bombshell and said she resigned from the agency, and was leaving in 3 weeks. I was so angry with her, but I didn't say anything. I was crying all the time in between our sessions and did not tell her, nor did I ever cry in front of her. I felt ashamed of myself for getting this emotional over her, I was very confused by my feelings, because it felt like a break-up even though I was not attracted to her. I was never able to tell her how I was truly feeling. At the end of our last session, she asked me if she could hug me. It was just like how you described your "goodbye" hug. (I hate hugging, as well). It was one of the best ones ever and I still find myself replaying it over in my mind once in a while. To be honest, it took me a good 7 or 8 years to get over this. In hindsight, I should have talked with current T about this, but I was ashamed to because I didn't want her to think I was "obsessed" with old T.
Fast forward to new T and it's time for me to move away for work reasons. I had been seeing her for about 5 and a half years at that point. The same horrible, wrenching feelings came up again. Before I knew it, it was our last visit before I moved away. I almost couldn't drive over to her office. This one had been with me for me through so much crap. My father had gotten sick and died, I had adjustment issues at my new college where I was trying to finish my bachelor's degree, difficulties with friends and my mom/sister, fears of intimacy, etc. etc. etc. She offered to do phone sessions with me after I moved away, but at that point I didn't want to because I was uncomfortable with that prospect. At the end, I just went for it and hugged her. She returned it, but I still feel bad for not asking first. I just couldn't help it, I was so emotional and like you I wanted closure. I thought I wasn't going to ever see her again and it was tearing me apart. Well, I did end up contacting her a few months later after I moved away, and 4 years later I am still her patient in treatment with her at the time of this post. We do phone sessions and I see her in person when I am home visiting. I have brought up my feelings about that last [but not really] visit and how I felt ashamed of hugging her, I said "I just got emotional". She told me she understood why I did it, and I don't think she was bothered by it. I know the day will come when it's time to end therapy for good—really for good this time—and I try not to think about that, I just try to appreciate and take in the relationship for what it is right now (as weird as that sounds).
One thing that helps me with this attachment stuff: I have a high school friend who is in training to be a clinical psychologist right now. This friend told me that in her graduate studies, they are required to go through therapy themselves...not just career counseling or mentoring, but real psychotherapy. Well, she told me at some point in her therapy, the therapist left and she was genuinely pissed off at her! She said it really hit home for her what it felt like to be on the client's end of things. I can tell from knowing her since we were kids that figuring out people, the science and reasons behind their behavior, and connecting with them is truly her passion in life. She really wants to help. So, what I am trying to say is that you have to try to believe that your current therapist really DOES care about you and thinks about you, they want you to get better and regain enjoyment of your life and all it has to offer. It's just that they can't reveal that to you because of the ethics of their profession. It's for our own good. They have to protect us because of the emotional instability that vulnerability causes. Reprocity from the therapist would ruin the purity of the whole thing, it would compromise everything you're working to achieve.
I hope this is of some comfort to you. Work on building your relationship with your new therapist. Your grief over old T will eventually soften with time. You'll never forget that person though, and that's perfectly OK.