Frigga had always loved children. Back when she was very young, she had told Odin that when they married, she wanted at least three. Odin was more ambivalent about children than she; he knew he had to have at least one, to carry on the bloodline, but other than that he never really gave it much thought. Children always confused him, he never really knew what to do with one. But still, he agreed to Friggas' wishes, because he knew it would make her happy, and he would deny her nothing.
When they were married, Frigga got pregnant with Thor right away. Everyone was excited, but it soon became apparent that this was not a normal pregnancy. She started getting sick often, something very rare for an Asgardian. The healers explained that the birth would be very difficult as a result, and it would become near impossible for her to ever have a normal pregnancy.
After Thor was born, Frigga expressed a desire to try to have more children in the future, hoping that somehow she could be cured, but Odin refused. One was enough, he said, He didn't want to lose her to something so avoidable.
Frigga was devastated. She loved Thor, of course, and treasured every moment with her child, but she lamented that he would grow up without siblings, and she would not get to see more of her children grow.
When the war with the Frost Giants came and ended in victory, Odin stumbled upon something in the the halls of Jotienheim. A baby. Something compelled him to lift the child, knowing full well that if he left it behind, it would most likely die of abandonment in its war torn realm. His first though was not of uniting the realms, not of using the child as a means of leverage or control, but of Frigga. He thought of her delight at another child, for he knew his wife would not care where a baby had come from; a baby was a baby to her. He took the boy home and showed her his discovery, asking her what they should do with the child.
Friggas response was immediate, taking the boy from Odins arms and into her own, already cooing softly at the child. They were to raise it as their own, of course. Odin asked her if it mattered that her new son was a Frost Giant, and Frigga merely shrugged, never taking her eyes off of the baby in her arms. So? She had asked, kissing the boy on the forehead. Oh dear, he must be hungry, who knows how long he was alone.
It was Frigga that named Loki, Frigga that sang him to sleep and showed him off, Frigga who hated putting her infant son down, preferring to keep him in her arms. Thor, too, expressed a love for his brother from the start, poking and prodding him, holding him with shaky arms as he tried to carry him around, always asking his mother, what does baby Loki want? Can I play with my brother?
As the boys grew older they began to fight, as brothers do, but playfully, and with a childlike competition. It was obviously they loved one another dearly, regardless. For a while Thor won every conflict with his strength, but as Loki grew he learned to use his words and later, his magic, to become a formidable opponent.
Odin made it no secret that Thor was his favorite. He figured it did not matter; Loki was Friggas favorite, so it evened out, in his mind. And while Frigga had forgotten that Loki was not her flesh and blood child, Odin never forgot, though he admitted it to no one, not even himself. Not to say he didn't love his second son; he did, but there was always a gravitation to subconsciously judge Loki on a harsher criteria than Thor.
Odin did not know why he didn't tell Loki the truth that day in the vault, when he had demanded to know why he was taken. It would have been easy to say it was for his mother, to make Frigga happy, and to save Lokis life, of course. He could have easily told the story of how Frigga had named him and cooed over him with a smile as great than any new mother- perhaps even greater- but he never did. He wondered, as he watched Loki be led away to the prison cell where he had been sentenced to live out the remainder of his life, if things would have turned out differently if he had told the truth.
"Loki-" He called out softly, and hesitated as his younger son turned his head. "I- never mind."