Warning: SPOILERS for Cobra Kai Season 2.
Cobra Kai season 2 introduced Tory Nichols (Peyton List) and many fans theorize that Cobra Kai's bad girl could secretly be the daughter of Ali Mills Schwarber (Elisabeth Shue) from The Karate Kid. Cobra Kai season 2 is set 35 years after the events of the original film, which was Ali's lone appearance in the franchise (thus far). But Ali is still fondly remembered by both of her high school exes, Johnny Lawrence (William Zabka) and Daniel LaRusso (Ralph Macchio). Cobra Kai has teased that Ali, who is now Dr. Ali Mills Schwarber, may return in season 3 - but, if she does, there's a chance Ali might be revealed as Tory's mother as well.
Tory joined the Cobra Kai dojo in Cobra Kai season 2, episode 4, "The Moment of Truth", and she immediately made an impact by going toe-to-toe with Johnny's top pupil, Miguel Diaz (Xolo Mariduena). Tory is the second female Cobra Kai student after Aisha Robinson (Nichole Brown), whom she quickly befriended. But Tory also immediately made an enemy of Samantha LaRusso (Mary Mouser), Daniel's daughter, who also happens to be Miguel's ex-girlfriend. Sam instantly disliked Tory and accused her of stealing her mother Amanda's (Courtney Henggeler) wallet at a beach club. Just like that, Tory and Sam became rivals just like Daniel and Johnny were. Their animosity continued when they had an altercation at a roller rink before Sam beat Tory at a drinking game during a party. The all-out brawl at West Valley High that ended Cobra Kai season 2 was instigated by Tory trying to get revenge on Sam for kissing Miguel, but the melee tragically resulted in Miguel being critically injured. Still, Tory went all-in with Cobra Kai and became a follower of Sensei John Kreese (Martin Kove).
The main reason that fans speculate Tory is really Ali Mills' Schwarber's daughter is because she introduced herself to Miguel as "Tory... with a Y." This echoed when Ali met Daniel in The Karate Kid and she introduced herself to LaRusso as "Ali... with an I". Given the fact that Cobra Kai has turned The Karate Kid into a generational saga, with Daniel training both his own daughter Sam and Johnny's estranged son, Robby Keene (Tanner Buchanan), in Miyagi-Do karate, it makes sense that fans theorize Tory isn't just the new creation she appears to be but that she's actually Karate Kid legacy character hiding in plain sight. The fact that Tory hates Sam also makes her the Johnny to Sam's Daniel and, if Ali really is Tory's mother, it neatly puts Daniel and Johnny's ex right in the middle of a new iteration of their everlasting rivalry.
However, Tory has also spoken about her home life and her stories seem to contradict that Ali is her mother. Tory told Miguel that she has a brother and that her (unnamed) mother was a waitress who was unfairly fired by her boss for stealing expired food for her kids. This contributed to Tory's severe worldview that "some people have it good but the rest of us? We have to fight for everything that's ours." This also explains Tory's disdain for "princesses" like Samantha who are lucky enough to have "rich daddies".
Ironically, when Ali was a teenager, she was one of those "rich princesses" Tory dislikes so much. So, if Ali really is Tory's birth mother, it means Tory is actually adopted and Ali gave her up for whatever reason. It's up to Cobra Kai season 3 to reveal if this is, indeed, the case and Tory Nichols is the daughter Ali Mills Schwarber. If so, it would also explain a lot about Tory's mentality and why she joined Cobra Kai while also creating a compelling new parent-child conflict for the series.
The strongest evidence against the Tory Is Ali's Daughter theory is that in Cobra Kai's DVD special features (via Twitter), executive producer Jon Hurwitz revealed that they named Tory "with a Y" because he and his fellow writers had dinner with Robert Mark Kamen, who wrote the original Karate Kid movies. Kamen has a daughter named Ali who spelled it "with an I" and named his movie's character after her. But Kamen's other daughter is named Tory "with a Y", and Cobra Kai's producers named Tory after her. But this link between Ali and Tory could still further manifest with the reveal that Tory Nichols is Ali Mills Schwarber's daughter in Cobra Kai season 3.