Okay, this is going to perhaps sound weird, but I'm going to put it out there:

I'm a hugger. I come from a family of huggers. I grew up around family friends who were all huggers. We hugged every time we greeted each other or parted from each other. So I guess I don't put much thought into hugging. It is as normal and spontaneous as shaking hands is to others I guess (not sure the comparison works because strangely enough I find hand shaking awkward).

However, I don't hug people willy nilly, but I guess I've just gained a sense over the years about which people are also huggers and which are not. I don't go up to people and hug them if I don't get that sense that they are comfortable with hugging. How do I know? No idea. Not sure I can explain it to tell you the truth. I do think it is a bit of an innate personality thing.

With a therapist though, even if they are naturally huggy people, they put that initiation in the place of clients and it makes sense that it is that way. Two of my therapists were big huggers like me. I think we started hugging practically from session one just because we were mutually huggy people and we sensed that of each other. I never asked them for a hug; we just started hugging. My last therapist was not a naturally huggy person, and it was longer before we started hugging, but now when we see each other on occasion, hugging is the first thing we do.

Sarah, I say all of that because you assume that just because a therapist is a therapist, then their hug is fake. While it might be true, it may just be very possible that your counselor is perfectly comfortable with hugging and does so naturally, even with clients, not just as some sort of obligation.

I'm a teacher, and I don't make it a practice to hug my students; I certainly don't initiate hugs. But I have some students who, like me, are huggy people, and at some point they sense it is okay to give me a hug and I am quite pleased to give them a hug back.

Perhaps understanding that some people are perfectly comfortable with hugging others and do so not out of obligation but because they welcome a good hug might help you rethink your counselor's hugs and be willing to accept them at face value instead of analyzing them.