Unfortunately, I think you are at the mercy of your dad.
Your profile doesn't say how old you are, but I assume you are under 18 right?
It may be best to just wait until you have your own place to live, although I'm sure that seems like forever to you now. When I lived at home, I had the hardest time trying to get my mom to allow me to have pets. We had an old cat and 1 dog. That was all that was allowed in the house.
Now, I have: 2 cats, 2 dogs, a bird, a ferret (my husband's), a ball python, 3 leopard geckos, a saltwater aquarium, and a baby on the way. If it weren't for the baby, I would have a brazilian rainbow boa now too. I'm think going to have to wait on the boa until I get used to having a child around. I think I must be rebelling against my mother still!
You can try letting your dad see that you are mature enough and knowledgeable enough, but chances are his mind is made up.
I wish you the best of luck!