Why does my parrot do this?

She seems really bonded to your dad. Parrots often do this, specially if there isn't another parrot around. She might even be trying to mate with him when she tilts her head back like that. Parrots often "fall in love" with one of their owners. There isn't much to do about it, if your dad would start ignoring her there is a risk she'll get very depressed.