One important thing people haven't realized yet: When Baelish claims his motivations for doing anything involving caring about Sansa or Cat he is completely and utterly full of shit. He is lying to manipulate Ned, Cat, and Sansa when he says these things. Don't look at what Littlefinger says look at what he does.
He knew starting a war between the Starks and Lannistes was likely to end in her death if the Starks lost. He does it anyway.
He lies to her about the Dagger used in the attempt on Bran's life, claiming it belongs to Tyrion. This results in her abducting Tyrion and personally pissing off Tywin, putting her directly into the crosshairs.
He later tries to convince Cat to trade Jaime for Sansa and Arya, even though this is a horrible idea and would have undermined Robb's ability to rule. This poisoned seed leads Cat to release Jaime without Robb's approval, undermining Robb's authority and directly leading to the debacle with Karstark.
Littlefinger brokers an alliance with the Tyrells and Lannisters, preventing Stannis from taking King's Landing. If he had, the war would have been over right there, and Sansa would have been perfectly safe with Stannis who had absolutely no reason to harm her and even tells Cat in the books that he plans to return Sansa to her once he takes King's Landing.
He does absolutely nothing to prevent the Red wedding or save Cat and/or Robb, even though he definitely saw it coming a mile away, just as we all did.
After he poisons Joffrey he tells Sansa he did it to avenge the Red Wedding. Really? Joffrey had nothing to do with the red wedding. Why kill Joffrey? Why not kill Tywin? Or Roose Bolton? Or Walder Frey? Because those don't fit into his plans. He needs Sansa's cooperation so he claims to be helping her get revenge. He's not. He also convienently frames Sansa for the crime so that she'll have no choice but to escape with him.
He kisses Sansa at the Eyrie, making sure Lysa sees it so she'll strike out at Sansa. This lets him murder Lysa in a way that keeps Sansa on his side. That's why he tells her he loved Cat before he kills her. To Manipulate Sansa.
And if that isn't enough, now he's having Sansa marry Joffrey 2.0.
Okay, so he's done all of those things to screw over Cat and Sansa and put them at risk. Can anyone name one single thing he's ever done that was a truly alturistic act for the benefit of Cat or Sansa that didn't also happen to advance his goals?
Littlefinger is a liar, and he's playing Sansa. Pure and simple.