Warning: SPOILERS for Cobra Kai season 3
In Cobra Kai season 3, Daniel LaRusso (Ralph Macchio) discovered that there's another side to Miyagi-Do karate that his late sensei, Mr. Miyagi (Noriyuki "Pat" Morita), kept a secret from him. Daniel returned to Okinawa for the first time since The Karate Kid Part II and he not only reunited with his former love interest, Kumiko (Tamlyn Tomita), but he also encountered Chozen (Yuji Okumoto), his arch-enemy who has shockingly turned over a new leaf.
Daniel-san was Mr. Miyagi's student and best friend from when they met in 1984 until the sensei's death in 2011. Daniel also learned the origin of Miyagi-Do karate in The Karate Kid Part II and it's an indelible part of the mythology: In 1625, Miyagi Shimpo Sensei, a fisherman, fell asleep from drinking too much sake off the coast of Okinawa. He woke up off the coast of China and then, 10 years later, he returned with a wife, children, and the secret of Miyagi's family karate. When LaRusso opened the Miyagi-Do dojo and set himself up as sensei, he showed his students the myriad new lessons Mr. Miyagi taught him that went beyond the iconic system of self-defense he trained Daniel-san in The Karate Kid movies. Naturally, after 27 years of training with Mr. Miyagi, Daniel assumed his sensei had taught him everything, but LaRusso found himself in for a rude awakening in Cobra Kai season 3.
At this point, Daniel-san is the embodiment of Miyagi-Do being strictly used for self-defense only, which is what Mr. Miyagi always taught "true" karate to be, and LaRusso was shocked when Chozen revealed that there was more to Miyagi-Do than Mr. Miyagi told him. But Chozen is also a Miyagi-Do sensei; he was trained by his uncle Sato Toguchi (Danny Kamekona), who grew up like brothers with Miyagi, and they were both taught karate by Miyagi's father - which sort of makes Daniel and Chozen "karate cousins". In Cobra Kai season 3, Chozen toyed with Daniel-san by making him believe they were still enemies, and he was a little miffed when LaRusso claimed that Mr. Miyagi taught him all there was to know about Miyagi-Do. Daniel had another thing coming because Mr. Miyagi did keep secrets from his student.
As Daniel discovered, Mr. Miyagi never told him that Miyagi-Do karate can also be used to kill because "defense takes on many forms." As Chozen explained, Miyagi ancestors once had to defend Okinawa from Japanese invaders and there was no option not to kill, so Miyagi instructors developed a system using secret pressure points to render their enemies helpless. Chozen demonstrated the secret Miyagi technique by incapacitating Daniel-san's joints and making him think he was going to murder him like he said he would back in 1985 - only to honk his nose the way Daniel did to Chozen at the end of their fight.
As hilarious as Chozen's prank at Daniel's expense was, it contained an important lesson for LaRusso: "If an enemy insists on war, then you take away their ability to wage it" - a maxim that could serve Daniel well against John Kreese (Martin Kove) and Cobra Kai. As for why Mr. Miyagi didn't want Daniel to know that his karate can also be used to kill, Daniel is probably correct that in the modern world, there is no need to use lethal karate. Still, Chozen gave him the Miyagi scrolls with the secret pressure points techniques, from one Miyagi-Do sensei to another.
What Mr. Miyagi valued most about karate, which he instilled in his students and Daniel, in turn, taught to his pupils in Cobra Kai, is the importance of maintaining your focus through difficult times and balance in all aspects of life. Mr. Miyagi never liked violence and he chose to embrace Miyagi-Do for healing and self-betterment. Thus, Daniel's sensei left the "secret" of how to kill with Miyagi-Do behind in Okinawa, but the way Chozen has lived his life since his darkest days in The Karate Kid Part II also shows Daniel that you can have balance in your life while still knowing how to take away an enemy's ability to wage war, if necessary.
Cobra Kai season 3 is available to stream on Netflix.