Personal attacks hurt people, mar communication, and end creativity. If they become part of a meeting's culture, they drive participants into making safe and perhaps useless contributions.
Approach 1: Speak to group
Set stage for group to enforce its culture by making a general comment. Look at middle of group and say:
"Just a moment. Let's pause here to calm down. I can tell we're upset about this. And we want to find a fair solution for everyone." (Take slow deep breaths and relax to model calming down.)
After saying this, pause a moment to let group respond. Often, someone else will support your request. Then continue as if everything were normal.
Avoid looking at attacker when speaking to group. Making eye contact acknowledges and returns power to attacker.
Approach 2: Explore for cause
Sometimes people throw insults from behind a fence of presumed safety. You can disrupt this illusion by saying:
"Chris, you seem upset with that."
"Pat, you seem to disagree."
"You seem to have reservations about this."
I realize these statements may sound like naive responses to an insult. However, such understated responses improve situation because they sound less threatening, feel easier to deliver, and preserve other person's self-esteem. Realize attacker may have viewed attack less seriously than it sounded.
These statements also transfer focus from target to attacker's feelings. And this is what you need to talk about in order to resolve dispute.