Medical professionals are trained to do their job in that manner. After years of being told to detach from emotions concerning the patient's situation, to be rational and observe only the facts, they rely mostly on results given by biochemical tests and medical machinery.
I relate to what you're describing, because I've felt that way many times. It's no coincidence you felt he was rushing to finish the visit, because it's been shown in many studies that doctors' offices purposefully overbook patients. Also, doctors are often visiting with one patient while waiting to hear back information regarding many other patients, and they'll make an educated and experienced judgement on which pending situation is the most serious. It doesn't mean their decision is always correct, or even fair to each patient.
I would suggest writing out a rough draft outline of your reasoning and conclusions, and once you get it as concise and to the point as possible, put the outline on an index card. Doctors tend to read information in a brief outline form, similar to what they see when they glance through a short page of blood test results. Look through your medical records and take note of how doctors want to see information presented to them. They want everything to the point, bottom line, and quick comparison logics of "if" and "then".
I've read that doctors don't like patients to bring in printouts or long lists of written symptoms, or pages of complaints. I can understand this dislike, but like you are saying, I needed to explain what I had observed. I've used this "index card" method on my own doctors when I felt they weren't really listening to me, and in most cases it's helped. If they ignored this, or any other attempt to get them to listen, then I found another doctor. When I visited the new doctor, and he or she asked what brought me in to see them, I said, "My previous doctor was too rushed and wouldn't listen to me."
Interestingly, the doctor I switched to a few years ago was thrilled when I handed him one index card with my outline notes, and a second index card with a list of medication and my other doctors' addresses and phone numbers. He said he wished all his patients would do that.