Sansa told Jon to wait until they had more soldiers, Jon knew there were no more but Sansa STILL didn't tell him about Littlefinger. Jon would've waited a little longer if only she had told him and would have never had to gotten saved to begin with.
She essentialy set him up to fail and then proclaimed herself the reason Jon won when she's actually the reason he lost.
You are correct, except she didn't even tell him to wait for more soldiers, just to wait, and knowing that having seen the undead horde Jon had this urgency.
And he asked to her face "Why should I wait!?"
I am against violence toward women, but in the ep following BotB he should have slapped the crap out of her imo. She not only set him up to fail, but to be killed alongside thousands of Wildlings.
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I think some people have argued that if Jon had a bigger army, Ramsey would never had met them out in the field. He would have stayed inside Winterfell and won.
This is a BS explanation.
She could have helped coordinate the Vale knights and Jon, letting him know when to expect them, and still draw Ramsey's forces out.
Think of this: what if Jon& Co had only showed up in front of WF 1h later, Vale knights charging in from the flank right after the Karstark forces charged?
Also, it didn't matter if they stayed in WF, Wildlings still had a Wun Wun who, covered by volleys of arrows fired into WF by Stavos led forces, could have charged in just the same.