The Klingon honor culture appears to work by people showing they're willing to fight at all time, but as long as everyone shows respect and maintains the attitude that they all major tough guys capable of epic battle, everything is fine. Sarek's point should have been taken to mean avoid saying "we come in peace". Instead you say it's a good day to die. You say everyone on your ship is eager to die in an epic battle worth of song. They say the same thing. Then they work out if they have an actual dispute. If not, they just respect each other as tough guys. I think that's what Sarek was saying. Burnham was itching for a fight and interpreted it that way. Maybe that's reasonable since the Klingons violated their territory. Maybe the Klingons would see anything other than shooting at them, even warning shots, as a sign of weakness. My thought is Burnham had conferenced Georgiou in to talk to Sarek, Georgiou might have found a way to project strength other than firing without warning. On top of this, as Xerxes said, T'Kumva isn't a normal Klingon. He was looking for a fight for political reasons. If the Federation had responded with strength, maybe he would have lost support. It's hard to say. It wouldn't have affected T'Kumva because his motivations were political. I do not see why the characters treat Burnham as if she started the war. Others have pointed out her mutiny had no effect on the outcome. Maybe in this time of war, people want a facile answer of "who started it," and mutineer is that answer. I think the audience is meant to sympathize with her, "Yes, you did something wrong, but you're not responsible for every tragedy related to it." It's like she's someone wrongly convicted on the felony murder rule. A bunch of people died while she was committing a crime. If things associated with her crimes caused the deaths, then she's responsible. But she's like a character who feels desperate and tries unsuccessfully to rob a store. She's quickly arrested. Someone dies in an unrelated car accident in the parking lot, and everyone blames her for it.