In EMT school the first thing that they drill into you is "scene safety." You don't want to become an additional victim of whatever situation you are responding to, no matter how much the scene calls out for immediate action. When I'm rolling up to a scene in my ambulance, I'm pretty good about taking this to heart.

If my kid is screaming out in terror or pain, it's a lot harder to do. That said, when I see my wife getting hysterical, it reminds me of the need to stay calm so that someone can make rational decisions, which helps. (Nothing disparaging intended towards my wife or her gender. That's just the rolls we play in our family. She gets hysterical, and when she does, its my job to take over making decisions that need to be made quickly.)