I work in a shelter and the other day my coworker and a client got into a protracted, heated exchange. The client suffers from some paranoia and delusions (mild) so cannot really be counted on to respond reasonably. The coworker felt disrespected because the client wasn't complying with their requests (they didn't involve safety issues or being disruptive to other clients though).
After a long shift, the client said something mildly snotty and my coworker got very confrontational about not being respected and they had a series of short arguments over the last 45 minutes of work which made me pretty uncomfortable.
I would like to suggest to my coworker that they "shouldn't" engage like that with a client because they are just escalating each other. They "should" just brush it off. I use quotes because someone told me that telling someone they "should" do something is contrary to the principles of nonviolent communication and I want to highlight that I want to avoid that word when we talk.
It was sort of one of those situations where my coworker wanted to be right more than they wanted to have a good outcome. We work closely together but I am fairly new, so we don't have a strong relationship yet.
How can I approach my coworker about this, using non-violent communication techniques?