There's a scene from TNG that shows this very well:
They are very calm about it, respect each other and resolve it in private. I always loved that scene, the way how they treat each other is just nice to watch.
In STD and STP, you wonder if there even is a chain of command, cause anyone can do anything without being punished, it's a madhouse.
Also, watching the first few episodes of STD, the one time someone does something that gets them punished, it's Burnham, who is accused of starting a war with the Klingons, even though they instigated it all.
This video puts it into context as well:
I can't wrap my head around this at all. They want to make him look like a fool and her like a quirky, spunky STRONK WAHMAN, but they achieve the opposite. She's an arrogant bitch, she doesn't even allow him to make a statement and then there's the subtle thing: He never interrupts her speech, but she never lets him finish even just one sentence.
If that chick is a captain, she must be the worst one I've seen, she'd get along nicely with Holdo from Star Wars.
Too bad, the actress is pretty good and she looks cute, but damn, this is a terrible screenplay.