Lemme rephrase myself so that it makes more sense. In a combat situation, you should not expect synths to stop and chat. Organics, ehhhhh, because they can still choose to surrender and stuff. Don't expect machines to back down because they have orders to follow to the letter; because they're machines. For the most part, if lethals are being exchanged between two parties, don't expect the other to give up the ghost because it wants to survive too. That only works on unarmed people; in which case I could defend you, but that wasn't the case here.
That is most definitely your personal opinion. You two were exchanging lethals and just told me that you had the chance to kill it. It kind of sounds like Garn and Jenn are saying in those logs. You infiltrated the core with lethal weapon(s), you are firing lethals in the core, and you SHOWED intent to kill and damage both station property and the AI itself (both being covered by AI laws). Your personal intent is irrelevant in this case because carding the AI is definitely not what you show by firing lethals at its turrets and there's no way he could've known that carding him was your true intent. Lethals is definitely the nuclear option, but it's a valid option regardless in this situation. If you weren't firing lethals, then that would be a totally different story, and using lethals would most certainly have been wrong. When you were showing intent to potentially destroy the AI, then gloves come off, and it needs to use every tool at its disposal (within reason as the situation escalates) to stop you. I'm sorry, but you should've been more prepared to deal with the AI.