Therapists provide care, but they may not care about you

Has anyone thought about this distinction as it relates to receiving care, but not being cared for or about?

Therapists are professionals, say, similar to a medical doctor, in that they provide care, but may not care for or about the person thereafter or outside the realm of the provision.

A doctor could save one's life, but nobody would ever expect them to then go on to care about them after the care was provided. Yet, somehow, as it relates to therapists, many want that during and after the care?

Why is that?