Hi seekersinking, IF you have borderline personality disorder you're NOT "defective" so don't let it worry you!! It may just mean that you need some different management skills/coping resources/support to address the things you're feeling/doing/thinking.
But I'd say that your therapist isn't right now actually diagnosing you with that anyway. Sometimes finding the right diagnosis/ways to help can just take a little exploration, and thinking about and ruling out or possibly in different things, and that's good. It can be trial and error.
And she's clearly trusting your judgement and insight to help her to help you the best way she possibly can.
Sometimes people can have symptoms of different things without even really realizing those symptoms/seeing them in themselves, so a bit of objective reflection can help in them identifying those things.
So maybe first of all have a think about the symptoms with an open mind (remember the diagnosis doesn't make you "defective") and then maybe work with your therapist on your thoughts and her thoughts relating to whether or not there's any room for potential or not.
It can take time for you both to come to conclusions you can agree with, but don't worry about that, it sounds like you have a very good overall relationship with her. Just stay open with her and it's just good that she hasn't stuck diagnosis's on you from day one without even getting to know you, and that she's taking her time to see any possibilities, and involving you.
Best wishes
Alison