There are ways to deal with such encounters in which you work with the angry patient and guide them through their emotions, and the accompanying volatility, to the point where it is possible to have a constructive, or at least manageable discussion with them.
Reason, although necessary, is insufficient alone. Patients who become angry typically will not respond to reason if only because they are so attached to controlling the encounter, intimidating the practitioner, are fearful of the environment or feel out of control, or want to shirk individual responsibility.
The anger itself must be reduced first. First, it is very important to perceive and understand the mindset of the other person. The given is that in the vast majority of situations the patient is really trying his or her best to resolve the problem. They may be confused, they may feel intimidated, they may be seeking answers to problems they don't easily understand. Thus, rule one is for the physicians to keep their own emotions under control. It is very important for a physician to communicate without rising to the same level of anger and/or aggression that their patient is exhibiting.
Next, the most important technique that can be employed in a volatile emotional environment is active listening. Paying close attention to the patient with appropriate body language will convey the unspoken message that the physician is attentive to the needs of the patient. Once the patient has vented fully, then the next step is to rephrase, in your own words, the content of what they said, and at the same time reflect an appropriate degree of concern and feeling and empathy. This is called "rephrasing the content, and reflecting the feeling."
When listening a critical skill for the physician is listening without interrupting, interjecting, or especially correcting the other person until they have finished what they have in their mind to say. To interrupt them when they are under the full power of their emotions can only further inflame them. Once they have fully vented, they are typically more amenable to a discussion.
Active and attentive listening should include telltale signs including eye contact, head nods, and brief intonations such as go on, right, yes, and other affirmative words or syllables. It is helpful to reiterate from the beginning that you are committed to making things right for them. Sometimes all that is then required is to ask what you can do to help this situation. And at all times, the physician should be deferential to the patient, maintaining the appropriate distance, staying out of the patient's personal space unless welcomed into it, and the physician should be mindful of what makes the patient comfortable or uncomfortable.
When the circumstance is such that the physician understands the patient's anger and views it as legitimate, then it is reasonable and appropriate to give the patient a straightforward acknowledgement. A physician can say, for example, "I can understand why that experience would make you angry". This response should be conveyed in a sincere and believable tone, reflecting the patient's feelings. Acknowledging their concerns with appropriate respect can pave the way to resolve the problem constructively. This does not necessarily endorse or agree with the patient's concerns or behavior, but rather legitimizes the patient's emotional feelings. Once the emotions are brought under control, then a mature and appropriate conversation can ensue.
If an actual apology is warranted in the case of a clear error or injustice, then the physician should apologize, but clearly only for their actions that were at fault. Often, patients will expand their primary complaints, and often the physician has little responsibility for these other perceived transgressions. Under these circumstances it is important to say something like, "although I cannot find an error that has taken place in that regard, I am still sorry that this situation has made you feel this way". This will avoid a re-escalation of emotions.
If there is only a portion of what they are saying that you agree with, you can say so, no matter how small that portion may be. In so doing you will often be able to defuse the anger without surrendering the facts of the larger issue. Once the anger is no longer an obstruction the remainder of the points of dispute may be handled more effectively and dispassionately.
If the encounter is not moving towards resolution, it may be because the patient is holding back additional points that are making them angry. In this situation it is important for the physician to convey to them that they should express everything that is bothering them. This will enable them to fully vent so as to reduce their strong and pent up emotions.
Defusing emotional encounters are a major deterrent to unnecessary litigation. Physicians and other health professionals should hone this skill.