Petyr is majorly in contradiction with the Identity premise. He changes his sigil for crying out loud.
He’s from a poor little place on the Fingers, and he was fortunate to be taken to the wealthy Riverrun to be fostered by Hoster Tully. There, Petyr, Catelyn and Lysa develop a wholesome childhood friendship that naturally evolves into young love. Lysa wants Petyr. Petyr wants Catelyn. Catelyn doesn’t know what she wants yet. In typical fashion, her father decides for her.
Petyr is too lowborn to marry a princess of Riverrun, so Hoster makes a better match for his daughter: The venerable Starks and their golden son, heir to WInterfell with enough charisma and hunkiness to make at least a few other women swoon, if the stories are true. Young Petyr is small but charming in his own way. His brand of charm seems to me to be described as that of the deviant, the hopeless romantic, the entertainer and/or the trickster. Brandon is everything that Petyr isn’t.
She remembered making mud pies with Lysa, the weight of them, the mud slick and brown between her fingers. They had served them to Littlefinger, giggling, and he’d eaten so much mud he was sick for a week. How young they all had been. (AGOT Catelyn V)
Littlefinger is driven like hell, and I think the thing that’s driving him is pure resentment. He’s resentful about his poor heritage. It cost him a chance to marry Catelyn. When Littlefinger visits his home at the Fingers, he comes across to me as neglectful of his home and the people who live there.
His peers have bestowed a humiliating nickname upon him and he has adopted it wholeheartedly. He pretends like the name doesn’t bother him, but I don’t buy it. I think the reason he takes the name is because it motivates him to climb at any cost. He wants to spite his enemies with his success.
I think Littlefinger has been biding his time and stewing over the unfairness of the world for the past fifteen years. I suspect he’s harboring a special hatred of House Stark in particular, which paints his lust for Sansa in a worrying light. She’s half Catelyn and half Stark. Half his greatest desire and half the target of his deepest hatreds. I think Littlefinger’s desire for Sansa is characterized in part by the pure and wholesome love he held for Catelyn as a boy. And I think it’s also characterized in part by a twisted fantasy to play out his revenge against the Starks by acquiring the Stark princess, who was born of a marriage that was only possible due to the unfairness that was inflicted upon Petyr as a brighthearted lovesick boy.
He was Petyr, her protector, warm and funny and gentle … but he was also Littlefinger, the lord she’d known at King’s Landing, smiling slyly and stroking his beard as he whispered in Queen Cersei’s ear. And Littlefinger was no friend of hers. (AFFC Sansa I)
I think Petyr’s Essential Identity in prophecies is the giant.
Loose Ends
“I have no one to talk with, Father,” she told him. “I pray, but the gods do not answer.” Lightly she kissed his hand. The skin was warm, blue veins branching like rivers beneath his pale translucent skin. Outside the greater rivers flowed, the Red Fork and the Tumblestone, and they would flow forever, but not so the rivers in her father’s hand. Too soon that current would grow still. “Last night I dreamed of that time Lysa and I got lost while riding back from Seagard. Do you remember? That strange fog came up and we fell behind the rest of the party. Everything was grey, and I could not see a foot past the nose of my horse. We lost the road. The branches of the trees were like long skinny arms reaching out to grab us as we passed. Lysa started to cry, and when I shouted the fog seemed to swallow the sound. But Petyr knew where we were, and he rode back and found us . . .” (ACOK Catelyn VII)
More characterization of Petyr being heroic in his youth. The sudden fog is characterized like magic. Could be due to childish fear, could be magic.
Apples and Dragons 