Take a Right - S2-E6
Tommy: Today was fun, Johnny.
Johnny: You still got some moves, man. You should stop by the dojo sometime.
Tommy: Yeah, right! Just like the good old days. And where'd all that time go?
Johnny: I don't know.
Tommy: You know, there was something I never told you. Didn't think you needed to know. Screw it. I was in love with Ali.
Johnny: What?
Tommy: Freshman year. We were in the same homeroom, used to talk all the time. I was building up the courage to ask her out when someone else struck first. Then I joined Cobra Kai. I wanted to have the balls that you have. But not the smell.
Johnny: I don't think I ever really got over her. I mean, I dated plenty of babes after, but I never really let my guard down with any of them, you know? Not like with Ali.
Tommy: You still got one thing that's more important than anything, Johnny.
Johnny: What's that?
Tommy: Time. You still have time.
Johnny: Yeah? Time for what?
Tommy: Meet someone new. Change your life. Do what you want to do.
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.
All Valley - S1-E7
Samantha LaRusso: Aren't we supposed to avoid fighting?
Daniel LaRusso: Sometimes you can't. Someday the fight may come to you. And I want to make sure you're ready. So today we're going to see what Miyagi-Do is made of.
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