Well, it seems as if the character being described in this situation is reacting to someone taunting her, and that’s what the narrator means by “Sometimes it’s just the way I say one word that gets her going”, and then retaliates to being ridiculed by punching the character responsible, or using some other form of physical violence. This must be what the narrator means by “she’s so quick with her hand it’s hard to imagine her being gentle to sick people.” We can use context clues to infer that the character being subjected to this teasing must have some type medical background because the narrator contradicts her actions —punching him— to when she consoles her patients.
I hope this helped you! I’m sorry for the late response.