Always, always, trust your gut. I've heard it mentioned before that friends sometimes just don't get therapy. I've even had a similar thing with a friend that thinks my T is a predator for hugging me. Sometimes it's best not to talk about it with other people since they aren't really trained to give a professional opinion.

A therapist has to care, so I don't get that... usually their caring is genuine unless they are some oddball sociopath, but you would have alarm bells sounding if that was the case. Don't re-examine the relationship if it feels good!