big kid

Let me set the scene: my cousin's two kids are visiting, ages 8 & 2.  It's morning and Owen and Emily are playing "Go Fish".  Donny wants to play too.  Aaand action:

Donny: I want to play.

Donny: I want to play too.

Donny: Ooowwwweeeennnnn, I want to plaaaaay.

Owen: you can't.  You're not a big kid.

Donny: yes I am. 

Donny: Ooowweennn, yes, I'm big kid too.

Owen: how old are you?

Donny: two.

Owen: That's not old enough to be a big kid.  Now don't come back until you're big.