There is a very small risk that showing empathy to a customer who is emotionally upset or angry will cause that person to escalate their ranting. It's a very very small risk, and it's almost zero if you use empathy properly.
One reason we created the CARP model was to remind people that the use of empathy with customers should involve a quick, touching on acknowledging the emotion present, followed by REFOCUSING back to the substantive issue.
In fact, if you use a very short, one sentence empathy statement, you'll see a decrease in angry verbal behavior.
Here's another way of putting it, from Perfect Phrases For Customer Service
Acknowledge Without Encouraging
When you deal with an angry or difficult customer, it’s importantto prove to him or her that you understand the facts surrounding the situation and the feelings the customer is experiencing. The catch is that “what you focus on,you get more of”—and you don’t want to encourage the customer to continue difficult or angry behavior that interferes with helping him or her.
“Acknowledge Without Encouraging” really involves the combination of two techniques
The first set involves using both empathy statements and refocus statements together. First, you acknowledge the feelings in a short sentence, and without stopping, you refocus or steer the conversation back to the problem and away from the customer’s emotions.
Similarly, you can do the same thing around demonstrating your understanding of the facts of the customer’s situation by combining active listening with refocusing. Reflect back your understanding of the customer’s situation, and then refocus back to problem solving.
The important thing to remember is the principle.You need to acknowledge the facts of the situation and the emotions, but you don’t want to dwell on them. Focusing on them results in longer interactions that tend to be more emotional.