You seem to be confused, if you convince him then what?, what does he have to even offer you afterwards?, condolences?.
Talking to your parents about this shit is pointless because they can't help you. Words don't matter, only actions matter.
Your father is both right and wrong, he's wrong that you still have a chance at 5'4" in this modern era where women have unlimited options. He's right in the sense that only your actions in life matter and just talking about these issues with your parents isn't going to do shit.
I really don't know why people waste their time trying to convince their parents about the black pill when you probably couldn't convince yourself from 10 years go (and they are an entire generation before you so they can't even comprehend your plight).