I'm upset that my dad won't put me on his car insurance
Why do you want him to put you on his insurance?
Because I want to drive his car down the mountain myself.
If you want to be able to drive, then you need to be able to take care of the costs involved without asking others to. Perhaps you could work out a plan for paying your dad back if he'll cover your up-front insurance cost, to show him you are reliable and willing to work.
Don't you think it's normal to not own a car, but to have your dad's car when you're 18?
What is normal for someone else may not be normal for you. Every family has their own standards when children are able to drive. If he is unwilling to put you on his insurance you can always work to afford your own.