Warning: SPOILERS for Cobra Kai season 3.
Cobra Kai season 3 kicks off with Miyagi-Do's reputation damaged because of the West Valley High brawl that ended season 2. The animosity between the students of the Cobra Kai and Miyagi-Do dojos erupted on the first day of school; by the time the violence was over, Miguel Diaz (Xolo Mariduena) was hospitalized in a coma, Samantha LaRusso (Mary Mouser) was also injured by Tory Nichols (Peyton List), and Robby Keene (Tanner Buchanan) on the run after he kicked Miguel off of a balcony.
Daniel LaRusso (Ralph Macchio), gave the Miyagi-Do dojo a higher profile than his mentor, the late Mr. Miyagi (Noriyuki "Pat" Morita), ever did (or possibly ever wanted). In The Karate Kid, Mr. Miyagi wasn't looking to train anyone in karate before he agreed to take on Daniel-san as his student so he could defend himself against Cobra Kai. Daniel was Miyagi's only student because they became best friends, although the old sensei took on a second pupil, Julie Pierce (Hilary Swank), a decade after he met Daniel-san. In Cobra Kai season 1, Daniel began training Robby, the son of his rival Johnny Lawrence (William Zabka), and he reopened Miyagi-D0 to new students in season 2 in order to compete with Johnny's Cobra Kai dojo, which was growing in popularity. But Johnny and Daniel's rivalry bled into their students, who developed their own grudges, and it all exploded at West Valley High with devastating results.
Cobra Kai season 3 begins two weeks after the West Valley High brawl and the LaRussos find they've taken the brunt of the blame for the violence at the school. Not only was their daughter Sam suspended but Robby is now a fugitive from justice. Public sympathy has rightly poured in for poor Miguel, but Cobra Kai and their nefarious sensei, John Kreese (Martin Kove), who stole the dojo from Johnny, somehow escaped consequences for the fact that it was Tory who started the fight in the first place. Instead, Miyagi-Do's reputation was in tatters and so is Daniel's car dealership, LaRusso Luxury Motors. As Daniel's wife Amanda complained, "Our name is poison. Turns out 'kicking the competition' isn't a cute tagline when your student literally kicks the competition over a railing."
Daniel realized how bad things were at the school board's public hearing when they announced all karate is banned at West Valley High and Miyagi-Do is the reason. As one parent yelled at LaRusso, "You're the one who taught those kids that Miyagi crap!" Miyagi-Do's core values that karate is used for self-defense only were totally lost because it was Robby who caused the biggest tragedy of the melee. Robby's mistake even reflected back on Daniel's own high school years when another parent said that he heard LaRusso was the real bully during the events of The Karate Kid back in 1984.
Of course, no one enjoys Daniel's misfortune more than John Kreese, who has hated LaRusso and Mr. Miyagi for 35 years. Cobra Kai's founder relished rubbing salt in Daniel's wound when he told LaRusso, "It must really hurt to see the Miyagi name dragged through the mud." In Cobra Kai, Mr. Miyagi has taken on an even more saintly status since his death and preserving his sensei's good name and reputation is very important to Daniel. Kreese is spot-on how much it stings LaRusso that he was unable to keep Mr. Miyagi and his legacy pristine during his renewed war against Cobra Kai.
Daniel-san is at rock bottom at the start of Cobra Kai season 3; he feels he failed Mr. Miyagi and his students, his business is in danger, and his daughter Sam is traumatized. After all, it was Daniel's decision to reopen Miyagi-Do and become a sensei the way Mr. Miyagi was to him. But somehow, Mr. Miyagi always did the right thing and knew just what to do in a bad situation, which is something Daniel still struggles with. As Mr. Miyagi would advise him, Daniel-san needs to regain his focus in Cobra Kai season 3, and that's the key to restoring Miyagi-Do's good name.