Burnham was more than anxious. Everyone on the shenzhou bridge was anxious about the Klingons, but no one else attempted mutiny or went along with Burnhams mutiny attempt. Considering that Burnham goes from a model starfleet officer about be offered her own command before meeting the Klingons to the behaviour that leads her to mutiny after meeting the Klingons, it's clear that it was the act of encountering a Klingon that triggered a pretty severe and uncharacteristic (in Georgiou's assessment) emotional response in her.
Well, I've already posted why I interpreted this series of events as an unorthodox conclusion to a series of logical actions, i.e. seeking Sarek's counsel, etc.
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There's a saying I heard once that i'm going to paraphrase, which is that people only ask for advice when they want to hear that they are right. Burnham getting Sarek's advice was done in the hopes that this would be enough to convince Georgiou to fire on the klingons.
But how do you know this applies in this situation? I mean, how do you know it for a fact? Was it stated somewhere in this episode or sometime later?
By the time we get to the finale, Burnham has changed as a person. She says it herself in her confrontation with Cornwell. That she made a decision at the expense of her principles at the start of the war and that she was wrong. It's entirely possible that the Burnham we see in the first episode would have gone along with Cornwell's plan, but the Burnham of the finale is different. Yes, she may still distrust the Klingons and be afraid of them but that doen't mean she is willing to endorse a plan to wipe them all out. Burnham says to Ash it would be simpler if she could hate the Klingons, but she can't and all she sees around her on Qo'nos is people living their lives and she can't bring herself to wipe out a peoples home.
But you'd think that if she really had been suffering from some psych disability that robbed her of her rationality as you've claimed, that she would have taken advantage of Cornwell's plan to get rid of the Klingons forever. After all, she had Starfleet's blessings, so that would have covered her. She would have been a hero and maybe still get her commission back. Of course, she would have had to live with the guilt, but an irrational person would not be likely to think of future consequences Instead, Burnham does what a rational person and competent Starfleet officer would have done, refuse to commit genocide.
The scene I am talking about occurs when Burnham and Tyler come across the group of Klingons playing a game. Tyler decides to join in to try and get information, as he remembers that Voq was quite good at this particular game. Burnham's stay for a bit but is shown to be visibly very uncomfortable at the Klingons laughing and being raucous and leaves. Ash eventually finds her and asks why she left and Burnham then confesses what happened to her parents.
Right, I remember. Burnham still has sad memories of her parents death and carries some guilt. The raucous Klingons brought on those memories, but instead of doing something irrational like pulling her phase pistol and threatening or charging the Klingons, she does what a rational person would do, she separates herself from them and regains her composure. Also, consider that Burnham seemed to be cool with individual Klingons all during the season.
But here's the real issue with this debate; the producers have never confirmed that Burnham suffered from any psych disability as an adult. There isn't one piece of on screen dialogue that confirms it. When
these writers (like most Trek writers) want us to know something important about a character, they leave no room for debate. MU Lorca, Voq/Tyler, Lorca's manipulation of Stamets, Lorca's hand in taking the ship into the MU, all of these things were open to debate for a time, but were eventually confirmed on screen one way or the other. The same is true of this PTSD thing. If it were really a part of Burnham's storyline, the writers would have confirmed it on screen.