Given that the climax of Game of Thrones season 6 is the ninth episode, "The Battle of the Bastards," the season spends much of its story establishing the parallels between those two bastards: Jon Snow (Kit Harington) and Ramsay Bolton (Iwan Rheon).
Both are bastard sons of noble Northern lords (or so they think), both have close relationships with dogs—with Jon's bond with his direwolf, Ghost, paralleling Ramsay's with his notorious hounds—and the two even share some physical characteristics, with Rheon actually having been considered for the role of Jon before his casting as Ramsay.
The key difference between Jon and Ramsay, of course, is their morality. While Jon is consistently portrayed as a good man, or at least a man consistently trying to do the right thing, Ramsay is perhaps the cruelest character in a show known for its cruel characters. With this in mind, one key death scene from early on in the season, before Jon and Ramsay even meet, helps to further their dichotomy.

The death of Osha
By the time Osha (Natalia Tena) reappears in season 6, it had been several years since we’d last seen her. Osha first encounters Bran Stark (Isaac Hempstead-Wright) after she and a few other wildlings fled south of the Wall. After the Free Folk threaten Bran, Robb (Richard Madden) and Theon (Alfie Allen) kill all of Osha's companions to protect the young lord, and keep Osha as a prisoner of Winterfell, where she later befriends Bran.
After Theon turns against the Starks and captures Winterfell, Osha helps Bran, his younger brother Rickon (Art Parkinson), and the simple-minded stableboy Hodor (Kristian Nairn), along with the Stark boys' direwolves, escape into the wilderness.
Osha butts heads with Reed siblings, Meera (Ellie Kendrick) and Jojen (Thomas Brodie-Sangster), after the two join Bran's party. Jojen, a fellow greenseer, encourages Bran to head north of the Wall to seek out the Three-Eyed Raven (Max Von Sydow) to hone his abilities. Osha, having previously escaped the North after fearing the undead invasion, is reluctant to return, so she and Rickon part ways as she takes the youngest Stark sibling into hiding.
After Ramsay becomes the Lord of Winterfell, Smalljon Umber (Dean S. Jagger), seeking to forge an alliance with the new Warden of the North, offers up Osha and Rickon, who are captured off screen between seasons 3 and 6. Later, Osha attempts to seduce Ramsay in order to lower his guard before killing him, but Ramsay is able to predict this thanks to a warning from Theon, and instead manages to stab Osha in the throat, killing her.

How does Osha's murder connect Jon and Ramsay?
Earlier in that very same episode, season 6 episode 4, "Book of the Stranger," a newly-resurrected Jon discusses his decision to leave the Night's Watch with Eddison Tollett (Ben Crompton). Edd feels as though Jon is betraying the Watch by leaving at this time of turmoil, given the impending undead invasion that the two witnessed in Hardhome and the inner struggles of the Watch regarding their new alliance with the wildlings, which had resulted in Jon's initial murder.
Shortly after reuniting with his sister Sansa Stark (Sophie Turner) and receiving a threatening letter from Ramsay, Jon departs Castle Black in order to take Winterfell back.
Osha's death reminds audiences of the consequences of Jon's decision to leave the Watch behind. While Jon likely has the viewers' sympathy initially due to his main character status and the fact that he's a likeble, easy-to-root-for character, Edd is also correct in that there is far too much to be done up North to abandon their cause at this moment.
In leaving Castle Black in Edd's hands, Jon is risking countless lives to the undead if he is not able to raise an army to stop them, especially putting the wildlings at risk.
Osha, meanwhile, is the first major wildling character to appear on Game of Thrones, predating even Ygritte (Rose Leslie), Tormund (Kristofer Hivju), and Mance (Ciarán Hinds). Her story begins with her escape from the frigid North and ends with her death at the hands of Ramsay Bolton, the exact kind of Lord Jon will never be. Ramsay is utterly apathetic about the plights of the wildlings, and would leave them to die at the hands of the White Walkers without a second thought, as would many other Lords of Westeros, if not for Jon's eventual intervention.
In depicting Osha's death at the hands of a man like this, Game of Thrones teases the grim fate that Jon, as their most charismatic advocate, could have left for the wildlings by taking the words "It shall not end until my death" literally.
You can stream Game of Thrones, House of the Dragon, and A Knight of the Seven Kingdoms on HBO Max.
