That's a hard place to be. I relate to your discomfort because I have had a hard time answering questions like that too. I think sometimes it takes a while to find those answers because they are deep inside and when you feel on the spot and pressured, you can't dig in and search your feelings. But the answers might come to you later. I think that some of your answers may have come to you when you sat down to write this post, because some of what you wrote would answer your T's questions. Maybe you could share what you wrote with her. Especially this part:

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Initially when she asked me what I want out of therapy, deep down is something that I want from her, I want her to be there for me and care about me. I want her to understand what I am going through. But I don't know if she truly can. I don't know if there is any point in me going to therapy. I don't see much point in a lot things. I've to go back and see her next week and I am afraid it is going to turn out the same as before with her asking me this question and it is like an ultimatum which I don't have the answer and I don't want to answer.

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Share the uncertainties too. That you don't know if she can understand you and be there for you, and that you aren't sure you see the point in it, but that you are desperate for some relief from your depression. Ask her what you will need to do to get better. Then you will have a better understanding of what she expects of you and what you can expect from her.