It's helpful when dealing with emotional people, but is not strictly for dealing with emotions. The whole point of parroting is to repeat back to the person, in your own words, what they are saying in order to ensure both parties are on the same page. When frustrated, people want to be understood. Yes, if you merely repeat back to them what they said you're doing it wrong. It needs to be in your own words and you need to reflect bullet points, not everything they say.