I think it's different to get certain needs met in therapy-- for understanding about what's tough for you, validation for an experience past or more in present, support for doing what is right for you and avoiding social pressure-- than to "depend" on the therapist for these.

I would not try to depend on someone who has said they don't want to be depended on. I think in a perfect world improving our social relationships is a great goal and, for me, an effect of therapy. But I think that the kind of validation and support and understanding I get for certain things in my life, like stressful work, there is not really a substitute for therapy in the real world. My therapist can handle discussions about the trauma that saturates the field I work in, but my friends really can't. I don't want to burden them with the details that can sometime haunt me or my frustration that we have no viable systems that can help change people's lives. My T can handle that.

There might be other analogs for other people, that a T can uniquely help in ways that friends and family cannot. That being said, I wonder if your T is more interested in helping you improve your relationships as opposed to being dependent on her, and that might be something worth discussing directly, as in "I want to have deeper, more connected, open relationships with my x and y," or whatever, if that is a goal for you.