Cobra Kai (2018)

The Rise - S4-E10

Johnny Lawrence: Robby. What's going on?
Robby Keene: I followed you.
Johnny Lawrence: What happened here?
Robby Keene: We're moving to a new location. Multiple locations, I think.
Johnny Lawrence: You kicked ass today. It could've gone either way.
Robby Keene: Yeah. Thanks.
Johnny Lawrence: Hey, it's just a match. Don't let it eat you up, trust me.
Robby Keene: It's not that, um, it's this kid, Kenny. I thought I could take him under my wing, be the mentor I wish I'd had when I was younger. When I saw him today it, uh, it was like looking in a mirror. And I realised I screwed everything up. And I had all this hate inside of me for you and for Miguel. And I thought I could use Cobra Kai to control that. But it just made things worse and now it's never going to get better.
Johnny Lawrence: That's not true. You had a good thing going with LaRusso. I got in the way of that. Don't blame yourself, you blame me.
Robby Keene: I'm sick of blaming you, Dad.

Take a Right - S2-E6

Trivia: Minor spoiler: In season 2, Johnny reunites with his old Cobra Kai buddies. One of them, Tommy, has been ill for some time. They go on one last ride together, and by the morning Tommy has died. Robert Garrison, who plays Tommy, went through something very similar. Robert had been ill for some time, and got together with the actors for one last reunion in this episode. He sadly passed away on 9/27/19, just months after the show aired.

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Show generally

Question: I've never seen the show so an explanation would really help. Why would Johnny open up his own Cobra Kai dojo? Since there was probably a lot of negative publicity due to how Kreese taught his students and how he attacked Johnny, a lot of people probably wouldn't go to a dojo synonymous with brutality but maybe to a dojo that taught karate the way it should be learned.