Continuity mistake: Miguel and Hawk are in the same class when Tory hijacks the announcement. When she meets Sam in the hallway, Hawk is now in the crowd behind Sam, but Miguel is just leaving the classroom and running through the halls.
Continuity mistake: During the school brawl, a teacher tries to break it up only to get body slammed. Hawk is flinching at this in the close-up. In the wide shot, he is kicking someone.
Continuity mistake: When Daniel threw his Crane Kick in the '84 movie, Johnny fell back and crawled away holding his nose as Daniel jumped around on one leg. But in the opening scene of this episode, Johnny is now prone on the mat as "Daniel" stands there in fighting position.
Strike First - S1-E2
Continuity mistake: During the pool party where Sam is hanging out with Yasmine and Moon, Yasmine holds her cup high in one shot but then low in the next.
Continuity mistake: While Daniel speaks with Cole at the car sales lot, the window of the truck beside them is up and down at least two times between shots.
December 19 - S3-E10
Continuity mistake: At one point during the first meeting of Vanessa and Ali, Vanessa is using a straw to play around with her martini glass. In the next shot, the straw disappears.
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.
Bishop73