My older daughter was a special kind of picky eater. When she was little and didn't want to eat what we were having, we tried the "It's either this or nothing" routine. She said "Okay!" and happily hopped down from her chair to go play. We said "Um ... that means NOTHING. No coming to us later and saying you're hungry." "Okay!" And she meant it, too. If she ever did get hungry later, we didn't hear about it. Meanwhile, I was fretting about starving my kid.
Both of my kids were like this. They'd happily go hungry for 4 hours between meals before they'd eat something they didn't want. Food was not a priority for them once they were older than 2. My son would happily eat just about any protein or fruit you'd put in front of him. But he was not going to have anything to do with vegetables other than brocolli (go figure). His pediatrician said to not worry about it but of course I did because I WANTED one of those kids who happily ate their salads, carrots, peas, beans. One of the Ped's nurses told me the problem was that he knew he just had to go a few hours before he could fill up on protein and carbs again so what I needed to do was only offer him protein for breakfast then at lunch and dinner, only offer vegetables and limit his milk to 8 oz at breakfast/lunch/dinner and afternoon snack. Let me tell you, a 4 year old can go for 3 days on a breakfast of a sausage link, an egg, a slice of toast and 4 glasses of milk without complaining about being hungry. After 3 days, my DH and I were both tired of vegetarian dinners and I was worried sick he was going to starve so reconcilled that he was going to never be a big vegetable eater. What I later discovered when he was around 6 was that most vegetables were too mild of a flavor for him. He likes bolder flavors so his favorites are brocolli, cauliflower, collard greens, cabbage and spinach, things I had been conditioned to believe were kid's least favorite vegetables so didn't cook often (except brocolli because that was his older sister's favorite veggie too). I mean if I couldn't get him to eat mashed potatoes, what chance did cauliflower have? Oh well, live and learn.