My daughter cannot stand green beans, and it's been that way ever since she started solid food. I remember sitting her in her high chair and feeding her an assortment of soft foods one night at dinner. Every time I tried a green bean she spit it out. Thinking that maybe it was the color that she was against, I tried hiding a single bean under a fork full of macaroni and cheese. Nope. She wasn't having it.
Periodically I would try again. Her brother loves them, so they are a frequent part of our dinners, but she always refuses. Finally the other night she announced to me that since she's three now, she likes green beans, and she specifically asked for them with dinner. Sure thing! I'm not going to deny a kid asking for a vegetable.
I was skeptical, but I served them. My son of course gobbled his up right away. His sister saved them for the very end, carefully eyeing them the whole time, but several times assuring me that she does like them. Finally she finished the rest of her plate, and took a bite.
My son was excited. Since green beans are one of his favorites, he really wanted her to like them too. As soon as she put it in her mouth he said enthusiastically "Aren't they good?!" Completely unaware of her expression, he went on the entire time she was chewing. "They're good, aren't they? Green beans are SO yummy! Aren't they yummy? Don't you like them?" Finally, exasperated, he said "Say something!"
I couldn't help but be amused as I watched, both by his enthusiasm and by her pained expression. She was so determined to finish the bean, and yet it was so very obviously a struggle. Finally she choked it down, and looking at me with a mixture of shame, disappointment, and pain, she said in a tiny voice "Mommy, I don't like it." She visibly relaxed when I assured her that she didn't have to finish them.
Frankly, I'm ok with her not liking green beans, and don't feel the need to force her to eat them. But that's only because there are plenty of other vegetables that she does love. And because I know first hand that not every person likes every vegetable out there. Most adults that I know have at least one or two that they won't touch.
For me it's celery. Never could stand the stuff. Mostly it's the texture, but the smell and the taste rank right up there. And it wasn't until I was an adult that I realized it was ok to not eat something that grossed me out, even if it was "good for me." I'll get my nutrients from all of the other vegetables that I like, thank you very much. And don't even try to disguise it, by the way. For years my parents tried the whole peanut-butter-and-celery thing. To me, it always just seemed like a gigantic waste of perfectly good peanut butter.
So yes, eat your vegetables. And make sure your kids are eating vegetables. But pick your battles, as they say. And remember that not everyone likes everything. There are plenty of options out there, so chances are you can find something that your kid does like.
For both of mine, ironically, the favorite vegetable of choice has always been celery. Go figure.