Every Mother's battle cry seems to be "eat your vegetables." How can you get your children to eat healthy foods if they insist that they're allergic to anything green?
First, remember that dinner is not the place for battle. Instead, simply offer your child the food, either by putting it on their plate or in a side dish. Before dinner, set a "rule" that your child doesn't have to eat the food, but there is also to be no whining, crying, etc. about consuming the food. Although as a parent you really want your child to eat the fruit or vegetable, you never want to force the "try it" bite. The child already has it in their mind that the food is unappetizing and likely will not enjoy that bite.
In fact, the best thing you can do as a parent is have them observe you eating the food and enjoying it. They know the food is there for them to try. Remember it often takes up to twenty tries before a child will accept a food, it takes patience! Furthermore, one week they may refuse a food they normally would eat. Children are notorious for "food jags", so just keep offering the food.
Also, never cater to the children's preference. Don't make a separate meal of chicken nuggets and French fries because that's all they'll eat. Tell them the food they can eat for that meal is on the table and that is it. If they do not want to eat the food, just tell them they will have to wait till snack time to have something else to eat. These are not easy strategies but when you apply them on a regular basis they really do work.
Foods should not be labeled as good or bad, including sweets. Once you take the "forbidden" label from foods, they often lose their allure. Sweets should never be used as a reward "if you eat your vegetables you can have a cookie". It is okay to offer your child something sweet every day and make it part of their meal as long as they are eating healthy most of the time. For example, they know they can have a cookie after dinner. They can choose to wait until later or have it immediately following the meal. Let them know that the cookie is all they get so they understand once it is eaten there is no more. Eating sweets often becomes a battle because many parents want their child to eat the 'healthy" foods first. But, it is never a good idea to use food as a reward, this teaches children to ignore their hunger signals (overeating in order to get a cookie) and contributes to obesity later in life.