Final answer:
The therapist crying with Julian is displaying empathy, which Carl Rogers considered essential in client-centered therapy to foster a deep therapeutic connection.
Step-by-step explanation:
Carl Rogers would identify the therapist's display of emotion as empathy. This characteristic is one of the three core conditions he believed were essential in client-centered therapy, along with genuineness and unconditional positive regard. When a therapist shares a client's feelings, it can create a deeper therapeutic connection and foster a healing environment. In this particular scenario, the therapist crying with Julian is a sign that she is fully present and attuned to his emotional experience, understanding his pain on a personal level, and communicating that his feelings are valid and important.