Armand doing the Twelve Steps makes perfect sense because this man is just so desperate to Belong and to be Good and he will twist and turn and warp himself and the world in a hundred ways trying to make that work.
And on one hand it is so painful watching him Really Earnestly Trying and watching everyone respond with rage.
On the other hand, in their own way Daniel and Lestat are both telling him to be sincere, and those apology notes were not sincere: they were classic fawn response "everything is my fault forever" and didn't actually apologize for THE THINGS DANIEL AND LESTAT ARE MAD ABOUT.
In Daniel's case the anger is straightforward: Daniel wants sincerity, Daniel wants the truth, Daniel wants to break people down and see the seething belly beneath. He met Armand at a moment where Armand was fully unhinged and hiding nothing, and since then (as far as he remembers) Armand has always been putting on a show. And after two years of Daniel miserably pining for him, Armand shows up with yet another show. Of course Daniel's going to be furious, and of course Daniel's going to push every button he can find because that's what Daniel does.
In Lestat's case it's easier to see his acts as purely hate-driven, but on third watch I actually think he too is demanding sincerity. "Be yourself" is a real statement. "Big Boss" is clearly catty and petty and all over the place (Armand having a bad hair day, since when) but the actual accusations are pretty clear: you want to control the narrative, you think you and you alone have the right to decide who is good and bad, you killed Claudia.
And Armand didn't apologize for any of those things, in fact Armand is still trying to control the narrative and still trying to decide who's good and bad, he's just moving himself to "bad" and moving Lestat to "good."
(side note gosh Lestat you sure do have a thing for controlling judgy self-flagellating men maybe you should explore that about yourself)
It's especially striking that Lestat knew lying would eat Armand up inside. It's easy to dismiss Armand as manipulative--and frequently he is manipulative--but that doesn't mean he's gleefully going around deceiving people. He's just frantically trying to be whoever he needs to be so people will love and accept him, because that's how he's survived all this time. He has no idea how to be himself, and he's probably terrified by the idea, since the message he's received over and over again his whole life is that being himself is Bad and Wrong and the only thing lovable about him is his looks (a cycle he then perpetuates by doing worse and worse things in order to either persuade people to love him, punish people for not loving him, or most vicious of all punish people for being loved when he is not.)