Öyle de söylenebilir.
Bir başka örnek de, bir websitesi veya bir kapı açılmıyorsa: it won't open.
Gizli bir if-clause varmış gibi düşün. It won't open (no matter how much I try.)
He won't give it back (even if I try.)
I think saying "he won't give it back" is a little stronger than saying "he doesn't want to give it back." The "won't" version conveys to me the idea not just that he doesn't want to give it back but also that he actually refuses to give it back and that you cannot make him give it back. You can say in English "I don't want to give this back to you but I suppose I am required to." But a sentence like "I won't give this back to you but I am required to" would not make sense.