My workplace is fairly old-fasioned, and (perhaps not coincidentally) thoroughly devoted to avoiding situations of high emotion. I attended a meeting once during which I was rightly yelled at, and afterwards my boss came by to tell me how sorry she was I was yelled at, and how I should not take that yelling personally, etc. etc. She seemed to think I would quit on the spot, despite the fact that I totally deserved to be yelled at.
I've never been in a meeting (yet) where tears were shed, but I think they would only inspire the same panic-faces and desperate topic-changing. It's a very weird workplace sometimes.
My previous workplace, I was known to both yell and vibrate with hatred, but the one time tears were truly in order, they did not come till after I had left for the night. (I spent two hours under the worst tension I've experienced in my adult life -- I say that advisedly, as a Red Sox fan -- and left knowing my job would end. It was only after, as I began to react to the tension, that I cried.)
I will say, however, that the above experience, with a male boss, and several arguments I've had with men, have led me to conclude that my crying in an argument will often cause men, and sometimes women too, to completely panic and end the argument immediately, as if I'd whipped out some kind of nuclear weapon on them. I find this unutterably irritating, because I want the argument to continue, and I hate the idea that someone would think I was using a physiological expression of emotion to manipulate an argument.
Sometimes, when I find an argument where is getting intense or heated, I will gesture or say something to "give permission" for the argument to go to that next level of intensity. It's sort of funny, doing this with my Flatmate's classmates, because they are law students, and chomping at the bit to kill me with their exciting new logic, but also shy about how much they may steamroll your average layperson without coming across as an asshole.
Like, "Give me liberty or give me death!!! ...If that's okay with you."