You could also put together some research about how straightening damages hair, and not only hair, but it can damage the skin underneath. Brazilian blowouts also release formaldehyde. They're not safe for anyone, in my opinion.
Something that always stuck with me was Chris Rock's documentary on hair. He does an experiment where they stick a coke can in the straightener chemical. It melts it--totally, and in 24 hours or so. If you can find it, maybe ask him to watch it before you continue the discussion.
I'm sorry your dad is so against your natural hair. I think you are taking a very mature approach to it, and while he may sound serious, he might not actually hold your permit hostage for it.
Averages out at 2b, ranges from 1c to 3a, very fine
Mane 'n Tail co-wash + leave-in
Clarifying shampoo every few weeks