From what you've written, you don't seem to feel the need to go through the diagnosis, and personally, from your description of what you're looking for in therapy, it doesn't seem like there is a reason for you to go through a formal process. How does your therapist describe getting this diagnosis as being helpful in your therapy? In other words, has she talked specifically about how she sees this knowledge as changing or enhancing your goals in any way? A lot of times, a therapist will need a diagnosis if they feel that medication will be helpful or if they want to use a specific approach to therapy (example: A diagnosis of Bipolar can lead to medication and significant improvement in a person's ability to respond to psychotherapy or a diagnosis of Borderline Personality Disorder can lead to a decision to recommend that the client engage in Dialetical Behavioral Therapy).

I would really recommend that you go back at least one more time and talk with her about exactly what you've said here. It seems that the relationship up to this point has been good, but has been slowly going in the wrong direction in your view. Let her know that. Get her to specifically articulate WHY she sees getting a diagnosis is important. If she can't do that, I'm guessing that she's just frustrated and feels that you are spinning your wheels in therapy and she's grabbing at something or anything. Getting a formal evaluation is expensive and she should have a pretty good explanation/assessment of why you need to go through that process and how it will improve or enhance your treatment. Good luck with whatever you decide.

PS You might be thinking why go back if I don't agree, but I strongly urge you to go back and assert yourself in this situation. It's fine to leave, but give yourself the chance to stand up for what you think or believe. It's often a great opportunity to grow in therapy and if she doesn't seem willing to listen and explain adequately, you know for sure it's time to move on.