SMG was given the hardest job out of all of the actors on the series, in that she was directed - at least initially - to not emote. The reasons for this never made a lick of narrative sense. Don't get me wrong - the idea of having a human raised by Vulcans is intriguing, for much the same reason that Worf (a Klingon mostly raised by humans) ended up being intriguing. However, the Spock's sister thing fucked everything up, because of Amanda. She was within the house, fully human, and should have been able to ground Micheal. It's not like the show ignored her either. I guess it's possible as a result of her two childhood traumas she just turned her back on her "human nature." But then there's the related issue of how Burnham could have served for seven years aboard the Shenzhou with Georgiou and not let loose a bit. Regardless, she was specifically instructed to not show her emotions - and even worse, to talk about them instead of showing them. Until the showrunners changed their mind and/or forgot.
When I thought that the writers had a plan (e.g., prior to the last episode) I presumed that what the writing was trying to tell us about Micheal Burnham was that she was, due to her Vulcan upbringing, basically lying to herself. That is to say, she was under the belief that she was a supremely logical, rational person. However, in truth she was more emotional than the average human being. For whatever reason her upbringing meant she didn't have the tools to handle her childhood trauma - suppression works for Vulcans, but it does not work well for humans. So instead of confronting things, she kept running away from how she felt - or trying to rationalize it as being the "logical course of action." Thus she made random-ass gut check decisions when put in a crisis situation, when a normal human who was a Starfleet Officer would have known enough to second-guess those decisions.
Unfortunately, the season finale made it painfully clear that was not their intention. Instead they picked up tattered threads to her character that had been totally unused since the second episode, and decided to run with that.