Echos, just remember you have a lot you are dealing with right now. Bringing up the rape and everything, having that to process again... just remember sometimes it's easy to repeat a trauma, i.e. this one person took advantage and wasn't there for you so surely this other person will be the same way.
I get being hurt your therapist wouldn't hug you. It takes guts to put yourself out there and ask, but you know what some therapists just don't hug. I think it's ******** too, but honestly I understand why and the reason is they can get sued and potentially even lose their license now a days for something like this. I know many won't especially with people who suffered sexual abuse because the hugs can trigger those bad feelings and memories even if you don't expect them to, it just really is much more of a delicate issue than you might expect, but I know it seems so simple and just human to hug a person.
I know it's hard but I do hope you see this therapist at least once more. If nothing else you can explain to him how his rejection felt and then he'll have to explain himself. I think it might be therapeutic to discuss, it could potentially bring you two closer. If nothing else and he really is incompetent, at least after this next session you'll know for sure and you can walk away without any doubts, and also having taught him something he'll hopefully remember for the next client like you who is sure to roll around. Finally, I think confronting him in and of itself will be a big confidence boost and therapeutic... that's what they say at least. Therapists are good people to practice confronting I think, there's not really anything he can do to harm you, and you are always free to walk away. They are sworn to your secrecy, so take advantage of that ya know

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I hope you feel better soon.