When Sandor Clegane rode on the tourney ground in "A Game of Thrones" Tourney of the Hand, Renly Baratheon and Petyr Baelish make a wager: 100 golden dragons on the winner. Renly calls out, cheeringly, that "the Hound looks hungry today", to which Littlefinger only replies that "he knows better than to bite the hand that feeds him". The result is known: Sandor unhorses Jaime Lannister, and Littlefinger loses the money. Sansa then tells him that she knew it would end that way, and Littlefinger asks her to tell him beforehand next time. This little episode tells us quite a bit about Renly and Littlefinger and their approach on politics.
|Ready to bite.|
Littlefinger at one point tells Sansa that you are either a player in the Game of Thrones or a piece on the board, and that's how he views people. Sandor Clegane is clearly not a player, therefore he must be a piece. Clegane's affiliation is Lannister, therefore he will obey the rules and let his master win. Renly, on the other hand, judges people on their character traits (although his priorities are not exactly the best serving for his purposes). He doesn't care much for previous loyalties if the person in question has something he wants (love, affection and splendor, mostly).
|Showing some love and passion.|
It so happens that Littlefinger is out off. Sandor doesn't want to be the piece the people imagine him to be. He fills out his role as Joffrey's hound well enough, but it seems he does so out of a lack of other possibilities and because it suits his life style and his sub-conscious desire to kill his brother Gregor. Littlefinger fails to see that, as he fails to see that people are their own agents from time to time. His masterpiece, marrying Sansa to Harry the Heir to claim the North, doesn't take into account that Sansa might be an agent of her own will, neither.
|Who would ever attribute agency to a girl like that?|
This might also be the reason why Littlefinger inspires no loyalty on his own. He has to buy them (them = the pieces on the board). His approach is very unpersonal. He has exactly two servants he seems to trust a bit, and both of them date back to his youth: Lothor Brune and the old Kettleblack. Renly, on the other hand, used his personal charms and empathy to bind people to his person. He fell when he misjudged a person he thought he knew his whole life - Stannis, who would murder him in the night. It's a common mistake. Littlefinger will fall because it doesn't even occur to him that someone he regards as inferior is able to make decisions for themselves. He proved it with Sandor, the "Hound" that bit the feeding hand, and he will from Sansa, I'm certain of it.
|I'd guess that's how she'll look at Petyr when she finds out what he's done in the past.|