With the remaining Starks in disarray, there will be no one around to protect Jon Snow's status as King in the North. The Northern lords already distrust him since he went to treat with Daenerys. His strongest allies are his siblings, and if each of them view each other as suspicious, Jon Snow is in trouble. Furthermore, this theory contends that Littlefinger has long deduced Jon's true parentage, as evidenced by him lurking around the crypts of Winterfell (there are many fan theories that state that evidence of Jon's parentage are down there at the tomb of his mother, Lyanna Stark). Perhaps Littlefinger is waiting until the most auspicious moment to reveal who Jon Snow really is — he wants to use this information to weaken Jon's alliances.