I was finding a site to find out how to get past this route, but what if I get a spoiler from the site? So I found this one, and I want to ask this question.
So, I can't pass Route 12 in Pokémon Y, a man is saying: "Hey, Trainer, not a good idea to leave the city when you still have pending matters with Korrina" And I don't know what to do next of this.
DON'T GIVE SPOILERS, I WANT TO KNOW HOW TO PASS.
Basically what Azelfeo said. Go to the Tower of Mastery, and do what Korrina requires of you. The Breeder should let you pass after that.
Hope I helped!