No matter how much you claimed to love me, you couldn’t have a frostgiant sitting on the throne of Asgard!
So notice that even AFTER their huge fight and even AFTER Loki finds out he’s adopted and he’s actually a different species and Odin basically sucks at parenting… even after all that, when Odin’s down for the count, Loki freaks right out and calls for help.
Because he still wants to be his Father’s son, even if he isn’t biologically.
don’t forget when he kills Laufey, he says “and your death came by the son of Odin.”
He still considered himself Odin’s son at that point.
And even after his fall, he still introduces himself as “Loki of Asgard”. In addition to that, he never says anything like “you’re not my brother”, just “I’m not your brother” as in he never actually disowns any of his family members, just himself.
Just thought I’d throw that out there.