This scene was actually when I went from feeling more or less neutral on Joan to actively disliking her.
Because wow, that was patronizing.
I loved that scene in Elementary.
1) Firstly, because it immediately deconstructs the “hero throws and breaks something in frustration” cliche (Sherlock throwing a glass slide in HoB, anyone?) it might even be seen as a parody of that cliche.
2) Secondly, because the dynamic is different between a man and a woman than it would be between two women or two men, the visual of a man smashing something in a temper in front of a woman can be taken as threatening or borderline abusive. Joan Watson immediately shows that she is not intimidated by Holmes’ behavior.
3) Lastly? One of the running themes of Elementary is the deconstruction of Sherlock Holmes as the solitary, antisocial genius, and his becoming a member of a community. Holmes’ gifts are given their due respect, but no one in Elementary plays the game of Because Sherlock Holmes is a Bloody Genius He Can Do Whatever He Wants So There. When Sherlock goes after Moriarty (“M”), Captain Gregson suspends him. When Sherlock doesn’t want to talk about his addiction, Alfredo says “You’ve got to get over yourself.” And when Sherlock behaves like a spoiled child, Joan tells him “Use your words.”
You see Joan patronizing Sherlock. I see a member of Sherlock’s community teaching him how to behave like an adult member of that community.
Popular media portrays men patronizing women constantly & it’s considered neutral, but a woman patronizing a man is enough to flip people into incandescent rage. Not saying that’s what OP is feeling, but a woman patronizing a man is definitely a hot trigger.
I also want to point out that throwing and breaking things is one of the ways many domestic abusers (statistically likely to be men trying to intimidate/control/harm women) exert dominance and threaten & control their partners. There is nothing like a display of violence and destruction to remind a person that said violence and destruction could be visited upon their person, you know? So there is ABSOLUTELY a power differential at play here, even if they aren’t romantically/sexually involved and even if the writers didn’t intend for there to be. So Joan responding in kind, in a calm demonstrative way, is a way of her taking control of a charged situation and pointing out that yes, he’s acting like a childish dick throwing a temper tantrum and she isn’t going to let that slide/excuse him/clean up his mess for him.