You weren't supposed to have a quirk... But when your father turned rogue and wanted to team with villains... You learned that you indeed had one.

Quirk Transfer

The ability to take. Use. Amplify. And morph quirks. First touch takes 0.5% of one's quirk. Amplification is 200% as if taking the full quirk. And Morph: Ability to mix. Match. And use them as your own.

After losing your mother. And taking your father's quirk. You're taken into UA where Nezu, of all people, take you under his wing. And your instantly brought into the Hero Course.

That's where Shōta Aizawa is teaching...