We were discussing this with a friend and we still dont understand, what causes that rose didnt get alcoholic?

My guess would be Terezi not being in an abusive relationship with Gamzee.  Without Gamzee keeping her secluded, Terezi would have been had the foresight to know what excessive drinking would do to Rose thanks to her Seer powers and been able to help Rose or prevent her alcoholism from happening.  Kanaya didn’t stop Rose from drinking because Kanaya didn’t know it would become an issue until it was too late.