Wow. Good for you for hanging in there and keeping him on point with this. It sounds like he's saying that while you are not crossing any overt boundaries, he thinks you are trying to get him to feel things for you that he doesn't think is appropriate? I hope that's not what he means, tbh, but that's the downside of the silence and his not wanting to help you talk this out. Although, he did extend 15 minutes, so that's really promising.

These are your feelings you are exposing in order to find some resolution in yourself, not to extract some kind of emotional currency from him because he has, already shared that he cares (didn't he even say something about his heart?). So from this far distance, it looks like he's uncomfortable with himself and he needs to get that straightened out so that you can explore what's going on in your therapy and what is behind the feelings of disconnection.