It's just part of the job. I've seen the nicest doctors get yelled at by the meanest patients, who sometimes aren't even paying a dime for their care. And for some reason it seems like the nastiest people we deal with often aren't the one's you actually feel sorry for, i.e. the cancer patient who has a few months to live. It's usually the family member that expects you to make their 89 year old dad you've been taking care of for 2 weeks suddenly live forever, or the 36 year old with some chronic pain syndrome overlayed on top of a long history of substance abuse that you have no concrete problem to address and can't justify pain meds for.
It sucks, but it's part of the job and part of the reason so many of us get callous about our patients. You have to brush it off, realize you deal with people in the saddest, darkest parts of their lives, and try to not let it shake you. And like Mimelim said above, it's nothing different from many other jobs. I was a career server for years and had sit by with a smile while people yelled at me for their fries being cold or their frozen margarita not tasting like it had enough alcohol in it. I wouldn't trade the job and respect I have now to go back to that life.