That when Sansa breaks her promise to Jon about revealing his parentage, she’s not just breaking an oath made in front of a heart tree and callously using him as a pawn against his will against the woman she loves. She’s also using him against another member of his family. The parallel to Littlefinger pitting her and Arya against each other over control of Winterfell is apparently lost on her.
Not to mention that if Lyanna and Rhaegar were married (at least in show canon), then she and Daenerys are also extended family. She’s just protecting her family, my eye.
Of course, we were cheated out of seeing the scene where she and Arya learn this. It logically would have involved some heartfelt discussion, Jon talking about not knowing who he is, Sansa and Arya having to see him in a different light and/or comforting him, Jon pointing out that Dany is his family, too, etc. Instead we just cut to the next scene because D&D weren’t up to anything with such emotional depth.