I myself was a picky eater (now that I'm older I eat a lot of foods so no longer picky). There was a time when the only meat I would eat was white meat chicken, and the only vegetable I would eat was corn or carrots. I admit I got catered to a lot, because if I didn't like something, I would just not eat. I think I freaked my mother out.
I have 2 kids, one picky and one that will eat pretty much anything. And yes, they were both raised the same way. I never make them eat anything, but they must at least try a bite. If they don't want to eat what I serve, they are always welcome to pour themselves a bowl of cereal. I just don't see the point of them starving, but I don't want to fix a separate meal either. So cereal it is.
My picky daughter is actually the worst kind of picky and it does drive me a little crazy. The worst kind of picky is that she actually eats a lot of different foods, but only prepared in one very specific way. Hamburgers must be thin, not too thick. Chicken can be grilled, but not fried or with any kind of breading. Raw carrots are fine, cooked carrots are not. Pasta can only be certain shapes. I never know whether she'll eat or not when we go somewhere because if someone says "we're having chicken and carrots" she may either scarf it down or refuse to eat altogether.
Yet, this is the daughter that will happily eat sushi (several different kinds), Thai curry, salmon, prime rib, chinese chicken salad, tikka masala.