First off, you don't find nutritionists at hospitals. You find Registered Dieticians at hospitals. Well, that may not be true in every state. but nationwide nutritionists are not regulated. Registered Dieticians are. but I do recall reading that some states do it differently.
Regardless of their title, in 2018, you would be hard pressed to find an RD that does not recommend a plant-based diet. I belong to Kaiser - and the whole HMO recommends Plant Based from top to bottom. In the hospital room and cafeteria, most of the food is plant-based. I'm going to guesstimate that it's like 90% vegan. Every once in a while you will see chicken or egg. You're more likely to get soy milk than cow's milk.
It seems like every day another study comes out reinforcing that American's eating habits are formed by tradition and not good science.
IF there is no convincing him, then you just say starting now you eating a plant-based diet. There has to be plenty of plant-based food in the house. Just avoid the animal products. If your parents make roast beef, green beans, and mashed potatoes, just eat the green beans and the mashed tomatoes. Make your own lunches and breakfasts. You dad can't force you to eat meat if you don't want to.
However, I think it would be best to never stop trying to convince him. Maybe make some bargains. You will do all the dishes this week if this weekend he watches What the Health with you. Or go to the library and get a WFPB cookbook. he can pick the meal and you'll cook it. Help with grocery shopping in exchange for some more vegan-friendly items like soy milk and tofu. Stuff like that.
The Vegetarian Resource Group has an FAQ on working with your parents. I would think this would be the best place to start.
http://www.vrg.org/teen/telling_your_parents.php
There are a bunch of teenage vegans who have videos on this subject in YouTube. I haven't watched any of them and I imagine that some may not be of any help at all. But you might want to check a few out. Bite Size Vegan is a well-respected adult YouTube vegan. She has a video on the subject.
http://bitesizevegan.com/vegan-life...-let-me-go-vegan-advice-from-real-vegan-kids/
Take your time, be patient and think long term.