Think about things logically.
The direwolves in Game of Thrones were central figures in the Stark clan; a symbol for each child's fate as George RR Martin's book series A Song of Fire and Ice progressed. Every major character is going to get a send-off of some sort. Well, to be honest this may be the first time we're genuinely interested in Dorne ever since Oberyn died, given that you're throwing them in with some other interesting people.
Now you got a pack, but Arya is still a lone wolf.
Now, here's some actual (circumstantial) evidence to back up my common sense theory. Because in addition to Nymeria, it is also Ghost that should have been seen in "Stormborn". She implored him not to go to Dragonstone, but quickly changed her tune when she realized that meant she would inherit Winterfell (her warm nod more or less said: "don't let the door hit you on the way out!"). After all - Jon and Arya were the closest of the siblings, were they not?
Although HBO has the sole rights to allow the live streaming of the hit series, several channels have already partnered up with the network to give fans around the world more ways to catch it live. That agenda was making her lose herself, even after she reaffirmed that she Was Arya Stark to Jaqen Hagar, and the two reminders from her past have corrected her course. In a scary situation that no mask will get her out of, Arya looks over to see that Nymeria is the pack leader.
After the trailer for the episode generated mass excitement among fans wanting to see the feisty Arya reunited with her beloved pet, the reality turned out to be somewhat disappointing.
Arya takes her friends advice and heads north and although Gendry hasn't shown up yet, Nymiria did. The direwolf belongs to the wild. In a flawless world, Arya and Sansa would reunite in Winterfell and there would be no tension, then Bran would show up from the Wall, and then Jon's beautifully haired head would pop up last, thus completing all of my hopes and dreams for a Stark family reunion. It could be the wake up call that a happy reunion with her family is "not you" for Arya as well, and like her direwolf her path isn't being domesticated. So much of Game of Thrones has been driven by Varys and Littlefinger, including the ascensions of Dany and Jon. However, it soon became clear Nymeria wouldn't harm her - despite the fact that she wouldn't stay with her. Perhaps the direwolf is destined to fight as well.
Ser Davos is arguably one of the shrewdest, most experienced and versatile knights in the Seven Kingdoms and as for Tormund, well, he would march into battle unarmed against an army of White Walkers.
While her arrogance has always been her greatest failing, she doesn't want to be Queen of the North in Jon's stead.