Chihiro is expecting to meet Haku and he doesn't show up. Then he does in dragon form, but he's not looking well at all. He's being attacked by small paper darts and he's obviously badly injured.
It turns out he's stolen a precious object (a seal) from Yubaba's twin sister Zeniba. We know it has extraordinarily powerful magic because Kamaji says of it "that's as powerful as it gets".
We're given good reason to believe that Yubaba made him do it because:
- He's Yubaba's servant
- He disappears from time to time, rumoured to be doing "dirty work"
- Stealing names (it's a personal seal with the owner's name) is something Yubaba does
- He's a good guy
But Haku might have his own motivation for stealing it:
- He's under Yubaba's control and wants to get free
- He is desperate: he's "tried everything" to remember his own name, which would enable him to get free
- It's powerful: maybe he can use the magic to break Yubaba's control
- Alternatively: maybe if he steals Zeniba's name in place of his own he can break Yubaba's spell.
- Yubaba is harsh and cruel but not dishonourable: she's bound by the promise she made to give a job to anyone who asks and keeps the terms of the work contracts she signs. But stealing from her sister would be dishonourable.
So, did Yubaba make him do it or did he steal it for himself?