Mr. Han: You've already proven everything you needed to prove. Why do you still want to fight?
Dre Parker: Because I'm still scared. No matter what happens, tonight, after I leave, I don't want to be scared anymore.
Sherry Parker: So... How many students do you have?
Mr. Han: Including Dre?
Sherry Parker: Yes...
Mr. Han: One!
Dre Parker: Mr. Han... Do you know you got a car in your living room?
Mr. Han: Sometimes the most important fights are the ones you avoid.
Dre Parker: Be kinda hot if I won this thing, huh, Mr. Han?
Mr. Han: Be kinda hot if you focused.
Dre Parker: Yeah, well, after that.
Mr. Han: Your focus needs more focus.
Mr. Han: What happened to eye?
Dre Parker: I ran into a pole.
Mr. Han: interesting pole.
Cheng: Just stay away from us! All of us!
Answer: Because Dre has finally earned Chengs respect. The other Fighting Dragons bowed to Mr. Han because in China bowing is shown as a sign of respect as they see that he is a better teacher and a kinder master then Master Li.
Since this movie mirrors the 1984 original movie, this is like how Johnny Lawrence (William Zabka) and the Cobra Kai's (excluding Dutch [Chad McQueen]) finally respect Daniel Larusso (Ralph Macchio), after the latter defeats Lawrence-The only difference is that the Cobras do not bow to Mr. Miyagi.