Kiba hates Naruto because he is the crush of Hinata so during the Chinin exams when they fight challenge him to a special type of fight down by the Inuzuka, it does have a name but only someone in the Inuzuka clan can challenge someone to something (could be a fight, running race, or some type of strength test) where the winner will become the Heir or Head of the Inuzuka Clan if they challenged the current Head or Heir or for their mate.
Eg Kiba wants Hinata, he fights Naruto and wins - if Naruto and Hinata get together Kiba can break them up by reminding them of this challenge and because it's a Clan thing no one can fight it after it's done.
Kiba's mother who is watched hears Kiba challenging Naruto, and shocks her head because Kiba forgot that he doesn't have a mate yet and because his the Heir of the Inuzuka clan, which means that both her and Kiba's sister Hana would become the mates of Naruto, and they would have to show Kiba what he lost by mating with their new mate in front of him.
