@ebrady98, you are a brave young person and even at 61 years of age, I can still hear my own parents judging me as a youth when I read your story. I spent most of my life as a fat person because I was made to eat whatever, but only in small amounts because I was fat and it did not matter if I was hungry still. One is supposed to be hungry on a 'diet' after all! I had a serious carb addiction, but when I quit grains, etc. (i.e. adopted a primal life) and ate paleo/primal, my health issues went away.
I am a university professor and researcher and am far from a crazy, 'out there' sort of person. I know that for me and likely most other people, living a paleo/ primal life is the only way to have health. Like your Dad, I also ended up thinking that red meat was bad and so on. I was wrong, and fat. I wish when I was 14, that I had your courage. You are totally right in your quest for health. I wish I could wave a magic wand to get your parents straightened out. I have no answers at the moment. All I can say is "Stay the course".
I coach high-level adolescent female athletes, and one of my biggest rules is to NEVER tell them they need to 'lose weight'. That's just asking for them to start with eating disorders, and is completely irresponsible as a parent or a coach. When we talk about food, it's only about how, comparatively speaking, their friends are cars and my athletes are fighter jets. They need high-quality fuel, and probably a lot of it, or they'll crash and explode. Keep your head screwed on straight through all of this, and do what you can to educate your parents. I don't see what the harm would be in letting you do 30 days of straight primal and tracking results (NOT just stepping on a scale).