Just keep offering and they do finally grow out of it. Both of mine refused to eat tomato based pasta ( who woulda thunk it?) about a year ago and now love it. We tend to put one of each veggie on their plate with whatever they do eat in the hope they will start eating it. We want them to see that it is normal and that is dinner - choose to only eat the meat? Fine but you might be hungry later which is too bad. As a PP mentioned it is important that they get a rounded diet but it is sooo hard. I cooked specifically for the kids for a loooong time, things like if I made pasta I would make it something that they would eat but they have outgrown that fussiness and now will eat what we eat! Both of mine went through that phase of living on air too - everyone told me they would grow out of it and they did! DD eats so much now I never would have believed it when she was 2!