Trivia: When Daniel goes to talk to Mr. Miyagi at the cemetery, we see that Miyagi was born in June and died in November. Pat Morita, who played Mr. Miyagi, was also born in June, and died in November.
Trivia: Miguel takes Sam to "Golf and Stuff", Daniel did the same thing with Ali in The Karate Kid.
Answer: Just like in the original film, some guys want that brutality. Johnny in part opens the dojo because of his past rivalry with Daniel and to train a kid that's being bullied. But also, other kids that are being bullied want to join in order to learn to fight back. Johnny is also teaching the Cobra Kai creed (Strike First. Strike hard. No Mercy.") so that's why he opens his dojo with that name and the old Cobra Kai dojo's past reputation is exactly what he wants to elicit.
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