After the second episode of Game of Thrones Season 7, Arya Stark is finally heading home to the North, temporarily swayed from her quest to kill Queen Cersei Lannister in hopes of seeing her family again. And while fans are thrilled at the prospect of Jon Snow & Arya's reunion on Game of Thrones, honestly it will probably never happen. Yes, it's disappointing, but the story just doesn't seem to be heading in that direction. First of all, there's a simple logistical issue. Jon's debating whether or not to travel to Dragonstone, and if the previews are to be trusted, once Sam's note about the dragonglass (which can kill White Walkers) underneath Dragonstone reaches Winterfell, Jon will be on his way to meet with Daenerys. So, once again, Jon is heading away from the place where his family members think he is, and Arya will likely wind up like Bran, who's been playing travel phone tag up at the Wall for about four seasons now.
Beyond logistics, a Jon/Arya reunion just doesn't seem to fit with the show's themes. Jon already had an emotional reunion with a Stark sibling: Sansa. Because the half-siblings weren't particularly close, their embrace was an easy way to show how far both of them had come since Season 1. Arya and Jon, who always had a tight relationship (he's the one who gave her Needle), would naturally be happy to see one another, but it's a repeat of what already happened in Season 6. Given that Arya and Sansa frequently clashed, if they are the two to meet at Winterfell instead, they have so much to discuss — Arya left King's Landing, while Sansa was trapped as a part of Cersei's court, and they both spent some quality time with the Hound.
And there's always a chance that Arya won't be able to return home, or, at least, won't be welcomed there. There still haven't been any consequences to her time with the Faceless Men, and her transformation into "No One." Even Hot Pie recognized her as "Arry," the alias she was using while undercover as a boy. She just reclaimed her identity as Arya Stark, and when she met up with a direwolf that was pretty clearly Nymeria, her former pet, the wolf rebuffed her. It's possible that Arya will find that when she returns to Winterfell, she won't have the homecoming she's hoping for right now. Arya has strayed significantly from the Stark ethos, transforming herself into the avenger of her good-hearted, if not wise, family members. She's not the upstanding hero that Ned or Robb was, but instead a vindictive, angry, and vengeful assassin.
Plus, let's not forget — George R.R. Martin's book series set the precedent of killing fan favorite characters. It would be shocking if Arya was among them — Martin put Arya on his list of five characters who will survive A Song of Ice & Fire, along with Jon, Bran, Tyrion, and Dany — but it's possible the TV show will break with Martin's plan and kill Arya before she's able to return home.
Meanwhile, Jon is on a totally different path: He's the King of the North, he's negotiating with Dany, investigating possible ways to defeat White Walkers and still hasn't found out about R + L = J, even though Bran saw his true parentage in a vision last season. And after getting raised from the dead, it's possible that Jon has a larger purpose — like becoming Azor Ahai, the "prince who was promised" and the hero who will come again to save the world from the White Walkers. Jon's on a path that intersects with the Starks only incidentally.
A reunion between Arya and Jon Snow would make for a touching Game of Thrones scene, to be sure — but with only a handful of episodes before the Season 7 finale and only a handful more before the series comes to an end, these two important characters have their own paths to complete, and they probably won't overlap.