I believe him. She is still his daughter. But she is an apostate from Islam. He will try to convert her back to Islam and if that fails the religiously-mandated penalty is death. He neatly sidesteps the question.
Saying that Muslims are required to kill apostates is a bit like saying Christians are supposed to stone adulterers. It’s based on a misunderstanding of doctrine. As a Christian I am not “pro-Islam,” and I believe that Islam is a false hope, as it does not bring about salvation through faith in Christ, so I’m not really defending Islam, so much as I am defending the truth, and the truth isn’t partisan.
Don’t confuse tradition in Islamic countries with actual Islamic doctrine. I personally don’t believe the girl, and I think she handled her situation badly.