Loki could have addressed any of what Odin said. How he knew his hands weren't clean, how he was responsible for his own actions in regards to the death of Baldr and the subsequent murder of Fimafeng -wasn't that what he had just said when he emphasized it was his choice, or how while Hod was dear to Loki he was still Odin's son, or even that Frigg was incredibly incompetent at demanding oath if she ignored something because it seemed far too.... well, she underestimated so much so often, did it matter?
He could have pointed out that the wyrd Odin clung to must have then dictated that Baldr be an insufferable douchebag. But that wouldn't help this conversation at all.
No, Loki knew what was coming, even if Odin didn't. He would either die or he would experience a fate worse than death. Personally, he'd rather die. Get that out of the way, then the Aesir would have comfort that their precious Ragnarok would never come. At least not by Loki's hand. He wanted assurance from Odin that his wife and children would be alright, but his blood-brother had yet to make any indication that they wouldn't be. Besides, they had done nothing wrong. Regardless of Skadhi's threat, no one would let her actually go through with it. Not with innocent children.
Sighing, he had things he needed said to his wife. “I know you owe me nothing, not now, but can you see to Sigyn? Please, as my blood-brother, I ask you not to help me, but to help them. They had no part in this. Can you tell Sigyn that I'm sorry and that...” Loki paused. The realization that he was likely not going to see any of them again pulled at his heart and stung his eyes. “that I love her and the boys.” Deep breath, Loki, he told himself. Deep breath.
Tears were blinked away. This was it, this was the end of it. He did love his wife completely and he'd never said it to her because of his own delusions involving love. That it was an illusion, a trick and nothing more. And now he was never going to see her again. At least not and still keep them safe.
“Tell her to take the boys and go to Lauer.” Odin would know what that meant. Loki was sending his family to his mother.