Okay, so I have name changed to avoid any potential recognition. I'm a therapist and this is highly unprofessional on the part of the therapist.
The sign you like your therapist and would want to be friends with them means that you found a therapist you 'clicked' with and you feel they hear and understand you. In a sense, excellent rapport is an excellent sign. HOWEVER, while it shows the therapist was (probably) doing their job well, one of the reasons it is unethical to be friends during or just after therapy is because this 'relationship' started with you telling them things, private and vulnerable things, that you wouldn't usually disclose at the start of a friendship - this means you made yourself vulnerable, which is absolutely okay in the environment of therapy sessions, but as a friendship, it has a power imbalance.
I get you - I really like so many of my clients and with some I do get the sense that we would be excellent friends.....but the therapist should be respecting his professional ethics and obligations - protecting you. I also sometimes feel quite sad when clients move on once feeling in a better place, because I love working with them, but that is part of the job. Therapists are human too, but we have to have professional boundaries.
I would report this therapist to his professional body as clearly he has professionally lost the plot and may do so again with someone else.
The only way I might conceivably remain 'friends' (more like just friendly contacts) with a client is if we are thrown together via eg. local sport, school gate, clubs and so on, but I would always keep a respectful eye on not being intrusive. Should a number of years have passed, then it's possibly less of a concern, but I would always be careful to make sure I'm not abusing my position of initial trust.
My doctor has children at the same school. We often chat and cross at parties and he's a hoot, but he's still my doctor, so I won't be meeting him for coffee.