Well, I was thinking how a lot of people are saying that one of the things that they don't like about Burnham is how she effectively attempted to mutiny and take over the ship, saying it was unusual for a Vulcan to do such a thing, well, I recently rewatched The Menagerie, and Spock effectively carried out a mutiny to return Pike to Talos IV, so it's not unheard of for a Vulcan, or in Burnham's case, a Human rasied as a Vulcan to act on their emotions to do what they believe is right.
I didn't have a problem with this on the grounds of "a Vulcan wouldn't do that". I think the reason it doesn't work is that it isn't properly justified, dramatically speaking. Burnham asks to be excused from a bridge in the middle of a crisis to call Daddy, who shares a tidy little story about how the use of preemptive force is sometimes logical, and Burnham makes a not-very-effective case for it to Georgiou. When that fails, she immediately jumps to the conclusion that she needs to assault her commanding officer and usurp command. Then she completely blows this, fails to marshal the crew to accomplish the simple objective she just betrayed her captain for, and then gets arrested by the captain because she apparently can't even get the nerve pinch right.
It's all delivered in such a rush that it leaves the audience's head spinning. The show tried to sell us on the bond between Burnham and Georgiou, in fact it's the only character relationship the pilot seems willing to set up, but it's thrown away in a matter of minutes, without any sign dramatized internal conflict or deliberation.
We've talked about a hypothetical alternative structure for this show where the first two episodes were instead the season finale. Imagine if we'd spent time with these characters, seen how they relate to each other at length, their struggles and victories and camaraderie. We'd have been in the headspace of the Burnham character when she has to make this terrible decision. And then imagine seeing it handled this way, with the entire arc of her betrayal taking place over a matter of minutes.
I understand that they were trying to accomplish a lot in the first episode and time was limited. But that doesn't excuse you from the rules of functional dramatic storytelling. If there's just not enough time for the dramatic buildup you need for your twist to land, you are starting your story way too late. The writers wanted the payoff but didn't want to do the work.
The actors were doing a heroic job of trying to sell these underwritten character arcs anyway, and the response they have inspired in some viewers is a testament to how good they are. They really deserved better writing behind them.