This is what I think happened after Brainiac explained the war to Superman. What happened before the war. What happened before all of it. Enjoy.
Brainiac walked in to Jor-El's room to have a talk with him. "Jor-El!", he yelled. "Ah, Primus! What can I do for you my robotic friend?", said Jor-El saying his actual name. He was very happy for his accomplishments of making peace treaties, but Brainiac wasn't happy one bit. "You've been making peace with our enemies?! Why?!", asked Brainiac in anger. "We have been at causing wars for far too long. It has to end for sometime", Jor-El answered. But Brainiac was getting frustrated about this. "Is that what your wife, Lara, would want, is that What Kal-El and his cousin would want?!" Jor-El hearing this question from Brainiac made him concerned. "Primus, listen to me, if we don't take a break from this, people can get hurt real bad. We aren't winning. Our children are on the verge of death." But Brainiac had enough of this. "So you're decommissioning me?!" Jor-El was saddened realizing what he's doing to Brainiac is wrong, but it has to be done.
"Yes, I'm sorry. I have to declare ceasefire.", Jor-El admitted. Brainiac was about to burst into rage. "Brainiac I know you want to help! But you can't. If you do, your causing planets than species harm.", said Jor-El. "YOU CAN'T DEFY ME LIKE THIS. WE WERE A TEAM. WE WERE TO WIN WARS. I WAS BUILT FOR WAR. I AM PROGRAMMED TO C.O.M.P.L.Y." Brainiac was filled with so much upsets. Why would Jor-El do that to him? Jor-El's heart sank. He was ashamed of himself for having to choose to treat his helpful friend Brainiac like this. "Brainiac this of the good we can do.", Jor-El says in a soft voice. "Please, I only want what's best for you. That's way your part of our family; The House Of El. Please Brainiac, I promise I will let you help us with your ideas. But things are to risky. There's a threats that are WAY to stronger than us."
Braniac doesn't say a word. "Brainiac?", Jor-El says in concern. He tries to pat his shoulder but Brainiac pushes his hand away. "Do not touch me, Jor-El!", said an angered Brainiac. "Calm down", Jor-El said. "I will not. You Kryptonians were supposed to be stronger than this. But NO you wanted to protect your little family and all of these people. Weak." Brainiac the walks away from Jor-El to leave the house of El. Lara sees Braniac walking away. "Jor-El, Primus, what's going on.",she said. "Brainiac what's wrong, what did he say to you.", she asked. "Brainiac please don't leave us, we're family." Jor-El begged Braniac to be reasonable and understand but Braniac was so broken hearted as a machine, even though machine don't have emotion, but you can see it and hear it in his voice. Jor-El would want to beg on his knees and apologize for giving Braniac such news like this if he had to, but can't.
"Family, huh? Well I'm done with that. If you want to play this game. I understand. I'm pretty sure Zor-El and or Kara would understand as well." After saying this, Primus Brainiac leaves. "Jor-El, what have you done?", Lara says as she is shocked about hearing all of that. "I wrongfully fired him. He's so hurt inside. I'm so sorry Brainiac, my friend.", says Jor-El.
Brainiac walking around the halls says something that he is about to do that's very evil. "So the Kryptonian Empire wants to throw my away like so much dross? They have another thing coming to them. I had it with all of this! They want to see me decommissioned? I'll show them decommissioned." Brainiac didn't take the news about Jor-El giving peace talks with enemies. He decided he wants to be an enemy himself. He just about had it with Jor-El and all Kryptonian life and their pathetic Krypton. He doesn't want anything to do for peace. Now he's turned evil.
The End
This is just a theory of how Brainiac reacted to Jor-El's doings after what he mentioned in episode 10 season 2. Have a nice day. I really enjoyed writing this.