Well first of all I never used the word "should." I said "want." I never suggested that my therapist was obligated to care about me.

More importantly however, while I know that you're trying to be helpful, insinuating that not caring about myself is a lack of work on my part is hurtful and harmful.

I don't have to work to care about others. Many of the people I care about struggle with a lack of self-worth and/or a lack of compassion for themselves, and I don't see myself as somehow "working harder" than they are at their recovery, and I don't think that they don't deserve my compassion or that they have to somehow earn my compassion by curing themselves of their mental illness/deep seeded issues caused by years of trauma before they're worthy of being cared about.
Compassion for oneself is very different than compassion for others. And putting the blame on me for somehow just not working hard enough only adds to the problem.
I can't just flip a switch in my brain and decide to feel compassion for myself just because I want to. That's the whole problem. It's no more helpful to tell me to care about myself than it is to tell me to be happy to cure my depression or tell me to stop worrying to cure my anxiety. And, given this, your comment was basically telling me that I don't deserve to be cared about. I really hope that was not the message you actually intended to convey.