I want my dad to pay a portion of our netflix subscription
Why do you want him to pay?
I can't afford to pay $15 for netflix and my dad is always the first one to watch stuff on the tv every night.
It's fine to expect others to share payment of streaming services if they also use it. Otherwise they are taking advantage of you.
I'm not in the position to make demands of him, so I'm going to pay it myself.
Just because he's your father doesn't mean you can't ask to contribute to the cost of streaming channels he uses and you pay for. You have every right to expect him to contribute.