I interpret 'breaking rapport' as doing something that makes the other person feel less connected to you. For example, bluntly contradicting them, dismissing something they said, teasing them when they are not comfortable with it, looking away while they are talking, or turning your attention to your phone. Anything that shifts the interaction from "we are connecting" to "there is distance between us."

Less connected is good. Also making the other person feel more awkward or uncomfortable with the interaction.

I suspect most people desperately trying to hang on to it, except with those they are good friends with. Unless they want out of a conversation. Although i may be projecting here.