pre s12 a little '12 Knew Missy didn't betray him' headcanoning was soothing in a 'sometimes i like it when we get nice things' but that is absolutely in no way canon and the doctor genuinely believed the master abandoned him (and everybody else) to die and this belief in her betrayal is the only thing that allowed Missy to succeed in fulfilling his ideal of goodness (without hope, without witness, without reward) because if he had known, had he suspected, then what Missy did was witnessed. Them becoming friends due to her goodness voids the true sentiment of her actions. (It doesn't. According to him it does though.)
The doctor's ignorance allows that one small bubble of time to exist where the master, despite everything counting against them, all the circumstances piling up together to make it so hard for her to do it, did something Good. I mean, I disagree with his rules on goodness, but as per the rules of the story that was written, Missy does succeed. The tragedy is, of course, that they can never be friends again because of it, because in the doctor's arrogance at deciding what is good and bad with no leeway, he demands she receive no reward nor have any witnesses to her triumph (simm doesn't count, he's literally her).
When Dhawan!master arrives on scene, he tries to murder the doctor and all her friends and then rubs it in her face that he feels deep in his hearts that murder and chaos is just It for him. It's what gives him the warm fuzzies. It's what he's Meant to be doing. He also rubs it in her face that he just Doesn't Have A Good Side. This is what we call targeted manipulation as he's deliberately trying to mentally torture her (and did a great job at it, too, lets be real).
13's reaction to him in s12 is her reacting to betrayal. This is 13 thinking all their work was for nothing and the master just lied and led them on to avoid being executed and that they didn't Care about their friendship, it was all just a big ploy. A huge lie. A betrayal of the highest order because this is what the doctor wanted the most in the universe and it was just a joke to the master. It also doesn't help that he is actively lying to her face about why he's acting the way he is the entire time he's on the show.
The doctor can't actually know what they don't know. I do not claim that 12 was being anything but arrogant in s10, I agree he was, I think his absolutely flagellating views on what can and can't be considered true virtue is a great massive window into why he's the absolute pinnacle of self hatred and depression, of course he hates himself, the biggest peacock in the universe who needs an audience like he needs air actually thinks that to be a truly good person you cannot be doing it for any kind of reward or recognition. What a stunningly depressing view into his mind.
But the point is, I guess, that these two are both the stupidest idiots in the universe and peak narrative tragedy. Unable to meet in the middle (doctor's fault). Self centered reaction to discovering best enemy's tragic backstory leads to deaths of billions and a metric ton of victim blaming and false idolisation simultaneously (master's fault).
They cannot speak honestly. They will not speak honestly. There is so much going on with them both i could write a dissertation. A total mess. But The Doctor Must believe the master betrayed and abandoned them, hence 13's ignorance, because otherwise everything Missy did means nothing.
