Having good emotional intelligence is one necessary tool. Being able to identify emotions, understand them, frame them logically. Down-regulating your own negative emotions is a big part of working with a team, as well as de-escalation, especially if the work may be wrapped up in ego (as I personally think software development is).

Another aspect is understanding the reasons for choices. Sometimes we're just ignorant of a better way, and we need to be gently led toward that way. Sometimes we're aware of a better way, but we choose a "less-good way" for good reasons. Without understanding the reasons, we're liable to react from a position of ignorance, even though we may feel like it comes from a position of superiority/authority. No matter the reason, patience is the most constructive virtue here.

Then there's the psychological flaws some of us have, like perfectionism, anger, impatience. Sometimes we need help to overcome these persistent conditions; mentoring is helpful, but so is counseling. I have spoken frankly (but with respect) with colleagues in the past who had some persistent issues, and they did take the feedback and improve themselves. Won't always happen, but many people do want to be better.

When someone is reacting poorly, if we understand that there is a reason they are reacting poorly (whether it be psychological, intellectual, social, or just having a bad day), we can react to it dispassionately and rationally, and help them calm down and work through the problem. And by "them", I also mean ourselves. :)