Very conflicted, and could use some advice!

Marley • im just trying to live happily please
So for a while now I've wanted to start working out, and eating healthier. I mentioned starting this to my Dad, and he laughed at me. Kinda a,"You? Working out? Yeah right." Kind of thing. And every time I mention it he laughs at me and it makes me rethink. He's constantly calling me fat even though I know I'm not. (I'm 5'6 and weigh 120 which isn't bad). I want to work towards a healthier me, but feel like I'm not being treated seriously and I really want to be. Any tips as to how I can overcome this?