My therapist doesn't mind tears at all, but I hate them. Makes me feel out of control. But after about 4-5 months with my therapist, I realized that I didn't need to hold on so tightly. I was in therapy to learn healthier habits and responses, and the tears were part of the work. As far as your therapist being annoyed or impatient, I think that we often make assumptions about what other ppl think, and we see it through our own warped context. Angel_090, in your opening comment of this thread, you suggested that you couldn't believe that it was worth anyone's time, or that they'd truly be interested. But you haven't even let him get to know you at all! I think he suggested not coming back because sometimes it takes a few tries for the patient to find some they can open up to. I'd suggest giving him a chance.
I'm not saying that this will work for you, but it worked well for me- introduce yourself on paper, in writing. Then take it to your appt and ask him to read it out loud. In the writing, tell him briefly why you are there, and what you hope to achieve. Then tell him what's holding you back, why you're afraid, what the worst thing is that your afraid to happen. While he reads it, just breathe. Whatever emotions that come up are totally healthy and not unexpected. That pile of knots and fears and pressure has to slowly be unravelled- you just haven't had time to discover that therapy is a safe place. It takes time, and courage, but we all believe in you!!